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**About this book :- **
**Vector Bundles K Theory ** written by
** Allen Hatcher **.

The first portion of this book takes these theorems as its goals, with an exposition that should be accessible to bright undergraduates familiar with standard material in undergraduate courses in linear algebra, abstract algebra, and topology.
Later chapters of the book assume more, approximately the contents of a standard graduate course in algebraic topology. A concrete goal of the later chapters is to tell the full story on the stable J–homomorphism, which gives the first level of depth in the stable homotopy groups of spheres. Along the way various other topics related to vector bundles that are of interest independent of K–theory are also developed, such as the characteristic classes associated to the names Stiefel and Whitney, Chern, and Pontryagin.

**Book Detail :- **
** Title: ** Vector Bundles K Theory
** Edition: **
** Author(s): ** Allen Hatcher
** Publisher: **
** Series: **
** Year: ** 2017
** Pages: ** 124
** Type: ** PDF
** Language: ** English
** ISBN: **
** Country: ** US
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**About Author :- **

Author ** Allen Hatcher ** was born in Indiana. After obtain his B.S from Oberlin College in 1966, he went for his graduate studies to Stanford University, where he received his Ph.D. in 1971.

Hatcher start his career in Princeton University Assistant Professor from 1973 to 1979. He was also a member of the Institute for Advanced Study in 1975–76 and 1979–80. Hatcher went on to become a professor at the University of California, Los Angeles in 1977.

From 1983 he has been a professor at Cornell University; he is now a professor emeritus. In 1978 Hatcher was an invited speaker at the International Congresses of Mathematicians in Helsinki.

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**Book Contents :- **
**Vector Bundles K Theory ** written by
** Allen Hatcher **
cover the following topics.

1. Vector Bundles

2. K–Theory

3. Characteristic Classes

4. The J–Homomorphism

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