Introduction.- Homotopy.- Homology.- Spectral Sequences of Fibrations.- Cohomology Operations.- The Adams Spectral Sequence.- K-Theory and Other Extraordinary Cohomology Theories.
Anatoly Timofeevich Fomenko is Chair of Differential Geometry and
Applications in the Department of Mathematics and Mechanics at
Lomonosov Moscow State University. He is a full member of the
Russian Academy of Sciences, and a member of the Moscow
Mathematical Society. He is the author of several books, including
Visual Geometry and Topology, Modeling for Visualization (with T.L.
Kunii), and Modern Geometry: Methods and Applications (with B.A.
Dubrovin and S.P. Novikov).
Dmitry Borisovich Fuchs is Professor Emeritus of Mathematics at the
University of California, Davis. He earned his C.Sc. from Moscow
State University, and his D.Sc. at Tblisi State University. His
research interests include topology and the theory of foliations,
homological algebra, and representation theory. His main body of
work deals with representations and cohomology of
infinite-dimensional Lie algebras. This work has consequences in
string theory and conformal quantum field theory as codified in the
mathematical theory of vertex operator algebras. He is the author
of over 25 articles, and has served as thesis advisor to several
well-known mathematicians, including Boris Feigin, Fedor Malikov,
and Vladimir Rokhlin.
“This book is a treasure trove for every mathematician who has to deal with classical algebraic topology and homotopy theory on the research level. … Its style is refreshing and informative, and the reader can feel the authors’ joy at sharing their insight into algebraic topology. … will be a useful addition to any mathematical bookshelf.” (Thomas Hüttemann, Mathematical Reviews, March, 2017)“This book covers all the basic material necessary for complete understanding of the fundamentals of algebraic topology … . This increase in the number of topics has made the book more convenient for serious students not only to extend their knowledge but also to gain insight into the interplay between these three subjects. … This book is designed to help students to select the level of learning subjects they want to reach … .” (Haruo Minami, zbMATH 1346.55001, 2016)
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