TY  - BOOK
AU  - Fomenko,Anatoly
AU  - Fuchs,Dmitry
ED  - SpringerLink (Online service)
TI  - Homotopical Topology
T2  - Graduate Texts in Mathematics,
SN  - 9783319234885
AV  - QA169 
U1  - 512.6 23
PY  - 2016///
CY  - Cham
PB  - Springer International Publishing, Imprint: Springer
KW  - Algebra
KW  - K-theory
KW  - Algebraic topology
KW  - Category Theory, Homological Algebra
KW  - K-Theory
KW  - Algebraic Topology
N1  - Introduction -- Homotopy -- Homology -- Spectral Sequences of Fibrations -- Cohomology Operations -- The Adams Spectral Sequence -- K-Theory and Other Extraordinary Cohomology Theories
N2  - This classic text of the renowned Moscow mathematical school equips the aspiring mathematician with a solid grounding in the core of topology, from a homotopical perspective. Its comprehensiveness and depth of treatment are unmatched among topology textbooks: in addition to covering the basics—the fundamental notions and constructions of homotopy theory, covering spaces and the fundamental group, CW complexes, homology and cohomology, homological algebra—the book treats essential advanced topics, such as obstruction theory, characteristic classes, Steenrod squares, K-theory and cobordism theory, and, with distinctive thoroughness and lucidity, spectral sequences. The organization of the material around the major achievements of the golden era of topology—the Adams conjecture, Bott periodicity, the Hirzebruch–Riemann–Roch theorem, the Atiyah–Singer index theorem, to name a few—paints a clear picture of the canon of the subject. Grassmannians, loop spaces, and classical groups play a central role in mathematics, and therefore in the presentation of this book, as well. A judicious focus on the key ideas, at an appropriate magnification of detail, enables the reader to navigate the breadth of material, confidently, without the disorientation of algebraic minutiae. Many exercises are integrated throughout the text to build up the reader’s mastery of concepts and techniques. Numerous technical illustrations elucidate geometric constructions and the mechanics of spectral sequences and other sophisticated methods. Over fifty hauntingly captivating images by A. T. Fomenko artistically render the wondrous beauty, and mystery, of the subject
UR  - https://doi.org/10.1007/978-3-319-23488-5
ER  -