Diagram Cohomology and Isovariant Homotopy Theory
Title | Diagram Cohomology and Isovariant Homotopy Theory PDF eBook |
Author | Giora Dula |
Publisher | American Mathematical Soc. |
Total Pages | 97 |
Release | 1994 |
Genre | Mathematics |
ISBN | 0821825895 |
Obstruction theoretic methods are introduced into isovariant homotopy theory for a class of spaces with group actions; the latter includes all smooth actions of cyclic groups of prime power order. The central technical result is an equivalence between isovariant homotopy and specific equivariant homotopy theories for diagrams under suitable conditions. This leads to isovariant Whitehead theorems, an obstruction-theoretic approach to isovariant homotopy theory with obstructions in cohomology groups of ordinary and equivalent diagrams, and qualitative computations for rational homotopy groups of certain spaces of isovariant self maps of linear spheres. The computations show that these homotopy groups are often far more complicated than the rational homotopy groups for the corresponding spaces of equivariant self maps. Subsequent work will use these computations to construct new families of smooth actions on spheres that are topologically linear but differentiably nonlinear.
Equivariant Homotopy and Cohomology Theory
Title | Equivariant Homotopy and Cohomology Theory PDF eBook |
Author | J. Peter May |
Publisher | American Mathematical Soc. |
Total Pages | 384 |
Release | 1996 |
Genre | Mathematics |
ISBN | 0821803190 |
This volume introduces equivariant homotopy, homology, and cohomology theory, along with various related topics in modern algebraic topology. It explains the main ideas behind some of the most striking recent advances in the subject. The works 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. The book then introduces equivariant stable homotopy theory, the equivariant stable homotopy category, and the most important examples of equivariant cohomology theories. The basic machinery that is needed to make serious use of equivariant stable homotopy theory is presented next, along with discussions of the Segal conjecture and generalized Tate cohomology. Finally, the book gives an introduction to "brave new algebra", the study of point-set level algebraic structures on spectra and its equivariant applications. Emphasis is placed on equivariant complex cobordism, and related results on that topic are presented in detail.
Algebraic Topology - Homotopy and Homology
Title | Algebraic Topology - Homotopy and Homology PDF eBook |
Author | Robert M. Switzer |
Publisher | Springer |
Total Pages | 541 |
Release | 2017-12-01 |
Genre | Mathematics |
ISBN | 3642619231 |
From the reviews: "The author has attempted an ambitious and most commendable project. [...] The book contains much material that has not previously appeared in this format. The writing is clean and clear and the exposition is well motivated. [...] This book is, all in all, a very admirable work and a valuable addition to the literature." Mathematical Reviews
Homotopy Theory: An Introduction to Algebraic Topology
Title | Homotopy Theory: An Introduction to Algebraic Topology PDF eBook |
Author | |
Publisher | Academic Press |
Total Pages | 367 |
Release | 1975-11-12 |
Genre | Mathematics |
ISBN | 9780080873800 |
Homotopy Theory: An Introduction to Algebraic Topology
Cohomology Operations and Applications in Homotopy Theory
Title | Cohomology Operations and Applications in Homotopy Theory PDF eBook |
Author | Robert E. Mosher |
Publisher | Courier Corporation |
Total Pages | 226 |
Release | 2008-01-01 |
Genre | Mathematics |
ISBN | 0486466647 |
Cohomology operations are at the center of a major area of activity in algebraic topology. This treatment explores the single most important variety of operations, the Steenrod squares. It constructs these operations, proves their major properties, and provides numerous applications, including several different techniques of homotopy theory useful for computation. 1968 edition.
Stable Homotopy and Generalised Homology
Title | Stable Homotopy and Generalised Homology PDF eBook |
Author | John Frank Adams |
Publisher | University of Chicago Press |
Total Pages | 384 |
Release | 1974 |
Genre | Mathematics |
ISBN | 0226005240 |
J. Frank Adams, the founder of stable homotopy theory, gave a lecture series at the University of Chicago in 1967, 1970, and 1971, the 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. Adams's exposition of the first two topics played a vital role in setting the stage for modern work on periodicity phenomena in stable homotopy theory. His exposition on the third topic occupies the bulk of the book and gives his definitive treatment of the Adams spectral sequence along with many detailed examples and calculations in KU-theory that help give a feel for the subject.
Combinatorial Foundation of Homology and Homotopy
Title | Combinatorial Foundation of Homology and Homotopy PDF eBook |
Author | Hans-Joachim Baues |
Publisher | Springer Science & Business Media |
Total Pages | 379 |
Release | 2013-03-09 |
Genre | Mathematics |
ISBN | 3662113384 |
A new combinatorial foundation of the two concepts, based on a consideration of deep and classical results of homotopy theory, and an axiomatic characterization of the assumptions under which results in this field hold. Includes numerous explicit examples and applications in various fields of topology and algebra.