Homotopy

Topology II Homotopy: and Homology. Classical Manifolds  eBooks & eLearning

Posted by AvaxGenius at Sept. 19, 2022
Topology II Homotopy: and Homology. Classical Manifolds

Topology II Homotopy: and Homology. Classical Manifolds by S. P. Novikov, V. A. Rokhlin
English | PDF | 2004 | 264 Pages | ISBN : 3540519963 | 26.2 MB

Two top experts in topology, O.Ya. Viro and D.B. Fuchs, give an up-to-date account of research in central areas of topology and the theory of Lie groups. They cover homotopy, homology and cohomology as well as the theory of manifolds, Lie groups, Grassmanians and low-dimensional manifolds. Their book will be used by graduate students and researchers in mathematics and mathematical physics.

Fiber Bundles and Homotopy  eBooks & eLearning

Posted by ksveta6 at Jan. 17, 2022
Fiber Bundles and Homotopy

Fiber Bundles and Homotopy by Dai Tamaki
2021 | ISBN: 9811237999 | English | 350 pages | PDF | 76 MB

Stable Homotopy Theory  eBooks & eLearning

Posted by AvaxGenius at May 7, 2023
Stable Homotopy Theory

Stable Homotopy Theory: Lectures delivered at the University of California at Berkeley 1961 by J. Frank Adams
English | PDF | 1964 | 80 Pages | ISBN : N/A | 7.4 MB

Before I get down to the business of exposition, I'd like to offer a little motivation. I want to show that there are one or two places in homotopy theory where we strongly suspect that there is something systematic going on, but where we are not yet sure what the system is. The first question concerns the stable J-homomorphism. I recall that this is a homomorphism J: ~ (SQ) ~ ~S = ~ + (Sn), n large. r r r n It is of interest to the differential topologists. Since Bott, we know that ~ (SO) is periodic with period 8: r 6 8 r = 1 2 3 4 5 7 9· . · Z o o o z On the other hand, ~S is not known, but we can nevertheless r ask about the behavior of J. The differential topologists prove: 2 Th~~: If I' = ~ - 1, so that 'IT"r(SO) ~ 2, then J('IT"r(SO)) = 2m where m is a multiple of the denominator of ~/4k th (l\. being in the Pc Bepnoulli numher.) Conject~~: The above result is best possible, i.e. J('IT"r(SO)) = 2m where m 1s exactly this denominator. status of conJectuI'e ~ No proof in sight. Q9njecture Eo If I' = 8k or 8k + 1, so that 'IT"r(SO) = Z2' then J('IT"r(SO)) = 2 , 2 status of conjecture: Probably provable, but this is work in progl'ess.

Homotopy Theory of C*-Algebras  eBooks & eLearning

Posted by AvaxGenius at Oct. 21, 2022
Homotopy Theory of C*-Algebras

Homotopy Theory of C*-Algebras by Paul Arne Østvær
English | PDF(True) | 2010 | 142 Pages | ISBN : 3034605641 | 1.83 MB

Homotopy theory and C*-algebras are central topics in contemporary mathematics. This book introduces a modern homotopy theory for C*-algebras. One basic idea of the setup is to merge C*-algebras and spaces studied in algebraic topology into one category comprising C*-spaces. These objects are suitable fodder for standard homotopy theoretic moves, leading to unstable and stable model structures. With the foundations in place one is led to natural definitions of invariants for C*-spaces such as homology and cohomology theories, K-theory and zeta-functions. The text is largely self-contained. It serves a wide audience of graduate students and researchers interested in C*-algebras, homotopy theory and applications.

Axiomatic stable homotopy theory  eBooks & eLearning

Posted by insetes at May 8, 2021
Axiomatic stable homotopy theory

Axiomatic stable homotopy theory By Mark Hovey, John H. Palmieri, Neil P. Strickland
1997 | 61 Pages | ISBN: 0821806246 | DJVU | 4 MB

Complex Cobordism and Stable Homotopy Groups of Spheres  eBooks & eLearning

Posted by Jeembo at March 16, 2017
Complex Cobordism and Stable Homotopy Groups of Spheres

Complex Cobordism and Stable Homotopy Groups of Spheres by Douglas C. Ravenel
English | 2003 | ISBN: 082182967X | 395 Pages | PDF | 5.5 MB

This book has served as one of the few available on the classical Adams spectral sequence, and is the best account on the Adams-Novikov spectral sequence.

Fibrewise Homotopy Theory  eBooks & eLearning

Posted by AvaxGenius at July 8, 2018
Fibrewise Homotopy Theory

Fibrewise Homotopy Theory by Michael Charles Crabb
English | PDF | 1998 | 344 Pages | ISBN : 1447112679 | 29.22 MB

Topology occupies a central position in the mathematics of today. One of the most useful ideas to be introduced in the past sixty years is the concept of fibre bundle, which provides an appropriate framework for studying differential geometry and much else. Fibre bundles are examples of the kind of structures studied in fibrewise topology. Just as homotopy theory arises from topology, so fibrewise homotopy the­ ory arises from fibrewise topology.

Fibrewise Homotopy Theory (Repost)  eBooks & eLearning

Posted by AvaxGenius at July 28, 2018
Fibrewise Homotopy Theory (Repost)

Fibrewise Homotopy Theory by Michael Charles Crabb
English | PDF | 1998 | 344 Pages | ISBN : 1447112679 | 29.22 MB

Topology occupies a central position in the mathematics of today. One of the most useful ideas to be introduced in the past sixty years is the concept of fibre bundle, which provides an appropriate framework for studying differential geometry and much else. Fibre bundles are examples of the kind of structures studied in fibrewise topology. Just as homotopy theory arises from topology, so fibrewise homotopy the­ ory arises from fibrewise topology.

The Homotopy Theory of (∞,1)-Categories  eBooks & eLearning

Posted by arundhati at July 10, 2018
The Homotopy Theory of (∞,1)-Categories

Julia E. Bergner, "The Homotopy Theory of (∞,1)-Categories"
2018 | ISBN-10: 1107101360, 110749902X | 284 pages | PDF | 2 MB

Rational Homotopy Theory  eBooks & eLearning

Posted by insetes at Feb. 16, 2019
Rational Homotopy Theory

Rational Homotopy Theory By Yves Félix, Stephen Halperin, Jean-Claude Thomas (auth.)
2001 | 539 Pages | ISBN: 1461265169 | PDF | 21 MB