Homotopy type and homology

by Hans J. Baues

Publisher: Clarendon Press, Publisher: Oxford University Press in Oxford, New York

Written in English
Cover of: Homotopy type and homology | Hans J. Baues
Published: Pages: 489 Downloads: 136
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Subjects:

  • Homotopy theory.,
  • CW complexes.

Edition Notes

Includes bibliographical references (p. [479]-483) and index.

StatementHans-Joachim Baues.
SeriesOxford mathematical monographs, Oxford science publications
Classifications
LC ClassificationsQA612.7 .B39 1996
The Physical Object
Paginationxii, 489 p. :
Number of Pages489
ID Numbers
Open LibraryOL965461M
ISBN 100198514824
LC Control Number96001777

  Chapter 8 of the book focuses mostly on calculating homotopy groups, which are an important aspect of homotopy theory, but most working algebraic topologists spend more time on homology and cohomology, which (classically) are more easily computable. It’s an open question whether they will be similarly easier in homotopy type theory, but we. Stable homotopy theory, J. F. Adams: On the Non-Existence of Elements of Hopf Invariant One, J. F. Adams: On the groups J(X)-IV, J. F. Adams: Stable homotopy and generalised homology, , Adams' blue book. J. F. Adams: Localisation and completion with an addendum on the use of Brown-Peterson homology in stable homotopy. My book Modal Homotopy Type Theory appears today with Oxford University Press.. As the subtitle – ‘The prospect of a new logic for philosophy’ – suggests, I’m looking to persuade readers that the kinds of things philosophers look to do with the predicate calculus, set theory and modal logic are better achieved by modal homotopy (dependent) type theory.   This paper defines homology in homotopy type theory, in the process stable homotopy groups are also defined. Previous research in synthetic homotopy theory is relied on, in particular the definition of cohomology. This work lays the foundation for a computer checked construction of homology.

Formally, a homotopy between two continuous functions f and g from a topological space X to a topological space Y is defined to be a continuous function: × [,] → from the product of the space X with the unit interval [0,1] to Y such that (,) = and (,) = for all ∈.. If we think of the second parameter of H as time then H describes a continuous deformation of f into g: at time 0 we have. This book offers a detailed presentation of results needed to prove the Morse Homology Theorem using classical techniques from algebraic topology and homotopy theory. The text presents results that were formerly scattered in the mathematical literature, in a single reference with complete and detailed proofs. The core material includes CW. An Invitation to Computational Homotopy is an introduction to elementary algebraic topology for those with an interest in computers and computer programming. It expertly illustrates how the basics of the subject can be implemented on a computer through its focus on fully-worked examples designed to develop problem solving techniques. The book begins with a development of the equivariant algebraic topology of spaces culminating in a discussion of the Sullivan conjecture that emphasizes its relationship with classical Smith theory. It then introduces equivariant stable homotopy theory, the equivariant stable homotopy category, and the most important examples of equivariant.

Publication type: Journals: ISSN: , Coverage: Scope: Homology, Homotopy and Applications is a refereed journal which publishes high-quality papers in the general area of homotopy theory and algebraic topology, as well as applications of the ideas and results in this area. The Mathematical Sciences Research Institute (MSRI), founded in , is an independent nonprofit mathematical research institution whose funding sources include the National Science Foundation, foundations, corporations, and more than 90 universities and institutions. The Institute is located at 17 Gauss Way, on the University of California, Berkeley campus, close to Grizzly Peak, on the. 16 hours ago  In a recent research seminar at my home institution, it was stated that the homotopy group functors $\pi_1, \pi_2, \pi_3, $ are not a generalized homology theory, and I'd like to know why. (ii) is there a costructure on homotopy (yes in many cases) sort of generalising cogroups etc. I have looked at the possible Eilenberg-Zilber type structures on simplicial groupoids and this suggests there may be some general principles behind the known cases of nicely structured cohomology.

Homotopy type and homology by Hans J. Baues Download PDF EPUB FB2

The book's principal objective--and main result--is the classification theorem on k-variants and boundary invariants, which supplement the classical picture of homology and homotopy groups, along with computations of types that are obtained by applying this theorem.

Research mathematicians in algebraic topology will be interested in this new Cited by: The book's principal objective--and main result--is the classification theorem on k-variants and boundary invariants, which supplement the classical picture of homology and homotopy groups, along with computations of types that are obtained by applying this theorem.

Research mathematicians in algebraic topology will be interested in this new Price: $ The book's principal objective--and main result--is the classification theorem on k -variants and boundary invariants, which supplement the classical picture of homology and homotopy groups, along with computations of types that are obtained by applying this theorem.

The author, a leading Homotopy type and homology book in algebraic topology, provides a modern treatment of a long established set of questions in this important research area. The book's principal objective--and main result--is the classification theorem on k-variants and boundary invariants, which supplement the classical picture of homology and homotopy groups, along with computations of types that are obtained by.

On the homotopy classification of 2-connected 6-dimensional polyhedra ; Decomposition of homotopy types ; Homotopy groups in dimension 4 ; On the homotopy classification of simply connected 5-dimensional polyhedra ; Primary homotopy operations and homotopy groups of Homotopy type and homology book cones ; Bibliography ; Index: Series Title.

"This book contains much impressive mathematics, namely the achievements by algebraic topologists in obtaining extensive information on the stable homotopy groups of spheres, and the computation of various cobordism groups. It is a long book, and for the major part a very advanced book.

Starting from stable homotopy groups and (co)homology theories, the authors study the most important categories of spectra and the stable homotopy category, before moving on to computational aspects and more advanced topics such as monoidal structures, localisations and chromatic homotopy : David Barnes, Constanze Roitzheim.

actually characterizes a homotopy type completely. This book represents a new attempt to classify simply connected homotopy types in terms of homology and homotopy groups and additional algebraic structure on these groups.

The main new result and our principal objective is the classification theorem in Chapter 3 on `k-invariants' and `boundary. This is very categorical, but it isn't specifically about homology and cohomology in topology.

If you're looking for something more directly related to (co)homology of spaces, then I'd like to recommend Switzer's book Algebraic Topology - Homology and Homotopy.

It has a nice treatment of homology and cohomology from the categorical perspective. Logical constructions in type theory then correspond to homotopy-invariant constructions on spaces, while theorems and even proofs in the logical system inherit a homotopical meaning.

As the natural logic of homotopy, constructive type theory is also related to higher category theory as it is used e.g. in the notion of a higher topos. Get this from a library. Homotopy type and homology. [Hans J Baues] -- This monograph represents an attempt to classify homotopy types of simply connected CW-complexes.

It provides methods and examples of explicit homotopy classifications, and includes applications to. This is a textbook on informal homotopy type theory. It is part of the Univalent foundations of mathematics project that took place at the Institute for Advanced Study in / License. This work is licensed under the Creative Commons Attribution-ShareAlike Unported License.

Distribution. Compiled and printed versions of the book are available at the homotopy type theory website, and. In homology theory and algebraic topology, cohomology is a general term for a sequence of abelian groups defined from a co-chain is, cohomology is defined as the abstract study of cochains, cocycles, and logy can be viewed as a method of assigning algebraic invariants to a topological space that has a more refined algebraic structure than does homology.

Book Description. The Handbook of Homotopy Theory provides a panoramic view of an active area in mathematics that is currently seeing dramatic solutions to long-standing open problems, and is proving itself of increasing importance across many other mathematical disciplines.

The origins of the subject date back to work of Henri Poincaré and Heinz Hopf in the early 20th century, but it has. This book explains the following topics: the fundamental group, covering spaces, ordinary homology and cohomology in its singular, cellular, axiomatic, and represented versions, higher homotopy groups and the Hurewicz theorem, basic homotopy theory including fibrations and cofibrations, Poincare duality for manifolds and manifolds with boundary.

Algebraic Topology — Homotopy and Homology | Robert M. Switzer (auth.) | download | B–OK. Download books for free. Find books. From the reviews: "The author has attempted an ambitious and most commendable project. He assumes only a modest knowledge of algebraic topology on the part of the reader to start with, and he leads the reader systematically to the point at which he can begin to tackle problems in the current areas of research centered around generalized homology theories and their applications.

Homotopy type theory offers a new “univalent” foundation of mathematics, in which a central role is played by Voevodsky’s univalence axiom and higher inductive types.

The present book is intended as a first systematic exposition of the basics of univalent foundations, and a collection of examples of this new style of reasoning — but /5(3). Aims and Scope Homology, Homotopy and Applications is a refereed journal which publishes high-quality papers in the general area of homotopy theory and algebraic topology, as well as applications of the ideas and results in this area.

This means applications in the broadest possible sense, i.e. applications to other parts of mathematics such as number theory and algebraic geometry, as well as. Type: BOOK - Published: - Publisher: University of Chicago Press Get BOOK J. Frank Adams, the founder of stable homotopy theory, gave a lecture series at the University of Chicago in, andthe well-written notes of which are published in this classic in algebraic topology.

We currently publish 20 peer-reviewed journals and two annual books dealing with various fields of current research in pure and applied mathematics. We also publish high-level mathematics and mathematical physics book titles, including monographs, textbooks, and several long-running book.

Algebraic Topology - Homotopy and Homology by Robert M. Switzer,available at Book Depository with free delivery worldwide.5/5(3).

Frank Adams, the founder of stable homotopy theory, gave a lecture series at the University of Chicago in, andthe well-written notes of which are published in this classic in algebraic topology.

The three series focused on Novikov's work on operations in complex cobordism, Quillen's work on formal groups and complex cobordism, and stable homotopy and generalized homology. Khovanov homology [khovanov_categorification_] assigns to a diagram D of a link L ⊂ S 3 a bigraded chain complex CKh ∗, ∗ (D; Z), whose homology groups, Kh ∗, ∗ (D; Z), are a link invariant.

The Khovanov homotopy type was constructed by Lipschitz and Sarkar as a refinement of Khovanov homology. Books J. Adams, Algebraic Topology: a Student’s Guide, Cambridge Univ. Press, J. Adams, Stable Homotopy and Generalised Homology, Univ.

of Chicago Press. Homology is a tool from algebraic topology which, in the usual category, provides an invariant of topological spaces up to homotopy type.

There are numerous flavors of homology theory, each of which involves ‘counting’ special objects in a particular manner. A book published on Decem by Chapman and Hall/CRC (ISBN ), pages.

Haynes Miller (ed.) Handbook of Homotopy Theory (table of contents) on homotopy theory, including higher algebra and higher category theory. Terminology. The editor, Haynes Miller, comments in the introduction on the choice of title. Nilpotence and periodicity in stable homotopy theory, also known as the orange book.

Nilpotence and periodicity in stable homotopy theory (Annals of Mathematics Studies, No ), Princeton, NJ,xiv + pp., $ISBN X. It is in print, and you can order it through Amazon books in paperback or hardback.

As of March,it is also available for download here. Floer homology; hence, the type Dbordered sutured invariant associated to (M,Γ,Z) is the type Dhomotopy equivalence class of BSD[(M,Γ,Z), and our contact invariant is a homotopy equiv- alence class of elements.

The main purpose of this book is to give a systematic treatment of singular homology and cohomology theory. It is in some sense a sequel to the author's previous book in this Springer-Verlag series entitled Algebraic Topology: An Introduction.

This earlier book is definitely not a logical prerequisite for the present volume. However, it would certainly be advantageous for a prospective reader 5/5(3). Algebraic Topology Homotopy and Homology by Switzer, Robert M.

and Switzer, R. R. available in Trade Paperback onalso read synopsis and reviews. From the reviews: "The author has attempted an ambitious and most commendable project.

He assumes.This book considers deep and classical results of homotopy theory like the homological Whitehead theorem, the Hurewicz theorem, the finiteness obstruction theorem of Wall, the theorems on Whitehead torsion and simple homotopy equivalences, and characterizes axiomatically the assumptions under which such results hold.In Pure and Applied Mathematics, B Homotopy invariants.

Homotopy groups Let M(X, Y) denote the set of continuous mappings between the topological spaces X and Y. Two mappings f, g ∈ M(X, Y) are called homotopic if there is a one-parameter family of mappings f t ∈ M(X, Y) depending continuously on t ∈ [0, 1] and joining f and g, i.e., such that f 0 = f while f 1 = g.