K-Theory and Characteristic Classes

This book offers a modern introduction to characteristic classes and topological K -theory, two foundational topics in algebraic topology. It incorporates contemporary tools such as category theory, spectra, and modern homotopy theory, making the material more accessible and relevant for today's graduate students. It is intended as an "on-ramp" to advanced study, emphasizing practical application over exhaustive theoretical background.

The book is not designed to be self-contained. It introduces essential tools from modern homotopy theory without delving deeply into their foundations, focusing instead on how these tools are used in practice. It occasionally cites results without proof, directing readers to external sources. This approach encourages students to develop research habits, such as consulting references and exploring topics independently.

Introduces K-theory and characteristic classes from a modern homotopical perspective Uses the contemporary language of homotopy theory and spectra to introduce classical topics Provides guidance for readers to complete their understanding

Autorentext

Inna Zakharevich is an associate professor of mathematics at Cornell University. She obtained her Ph.D. at the Massachusetts Institute of Technology, and held postdoctoral positions at the University of Chicago and at the Institute for Advanced Study.  Her research is primarily in the fields of algebraic K-theory and scissors congruence.

Inhalt

A geometric beginning.- Formal constructions and fundamental examples.- Classification of vector bundles.- Some crucial players.- The Euler class.- Characteristic classes.- Cobordism invariants.- Bott periodicity.- Topological K theory.- Adams operations.- Next directions.- Appendix A.