Cohomology Operations and Applications in Homotopy Theory (Dover Books on Mathematics)

Book Details

• Publisher: Dover

• Author: Martin C. Tangora

• Language: English

• Edition: 1st Edition

• ISBN: 9780486466644

• Pages: 224

• Cover: Paperback

• Dimensions: 8.5 x 5.4 x 0.5 inches

About The Book

"Cohomology Operations and Steenrod Squares" by Martin C. Tangora is a pivotal text that dives deep into the world of cohomology operations, an essential technique in algebraic topology. These operations are used to enrich and supplement the algebraic structure of cohomology rings, playing a critical role in advancing homotopy theory and various geometric applications. Through this work, Tangora provides both theoretical insights and practical methods that have greatly contributed to the progress in algebraic topology.

The book centers on the most important type of cohomology operation—the Steenrod squares—detailing their construction, proving their key properties, and offering a variety of applications. Readers will find several techniques for homotopy theory, including valuable computation strategies. In the later chapters, special attention is given to calculations within the stable range, enhancing the practical applicability of the book. Furthermore, the text introduces influential methods developed by Serre, Toda, and Adams, and includes detailed computations to demonstrate their use.

Designed for those with a solid foundation in cohomology theory and some familiarity with homotopy groups, this text provides a comprehensive introduction to these advanced concepts. It is an indispensable resource for students and researchers looking to deepen their understanding of algebraic topology and homotopy theory.