Pdf Vector Bundles And K Theory Springer

Bonisiwe Shabane

-Nov 3, 2025, 2:07 AM

pdf vector bundles and k theory springer

The plan is for this to be a fairly short book focusing on topological K-theory and containing also the necessary background material on vector bundles and characteristic classes. Here is a provisional Table of Contents. At present only about half of the book is in good enough shape to be posted online, approximately 120 pages. This is available as a pdf file here. (I have reformatted this with narrower margins for a better reading experience on devices like an iPad, but for a paper copy with more standard size margins try printing at 85-90 per cent of... What is included in this installment is:

Much of this material is already well covered in other sources, notably the classic books of Atiyah (K-theory) and Milnor & Stasheff (Characteristic Classes). These books are still in print, although they have become somewhat expensive. Eventually I intend for the book to include a few more things that aren't readily accessible elsewhere, such as the full story on the stable J homomorphism. What is posted now is Version 2.2, dated November 2017. This is a minor revision of Version 2.0 from January 2003, with the addition (in 2017) of a section 3.3 giving the obstruction theory definition of Stiefel-Whitney classes. You have XXXXXX left today.

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More information in the FAQ. (might require browser verification — unlimited downloads!) Help out the community by reporting the quality of this file! 🙌 Part of the book series: Classics in Mathematics ((CLASSICS,volume 212)) In Chapter 4 we defined the notion of a fibre bundle (a locally trivial fibration); in this chapter we consider an important class of fibre bundles—those for which every fibre has the structure of...

We show how equivalence classes of such vector bundles over a CW-complex can be used to define groups K*(X) in such a way that K* becomes a cohomology theory. This is a preview of subscription content, log in via an institution to check access. Tax calculation will be finalised at checkout Unable to display preview. Download preview PDF. Tags: Математика Топология Алгебраическая топология

Glenys Luke, Alexander S. Mishchenko (auth.) 1243 Schamberger Freeway Apt. 502Port Orvilleville, ON H8J-6M9 Part of the book series: Texts and Readings in Physical Sciences ((TRiPS,volume 19)) The aim in the first part of this chapter is to understand the basics of Vector bundles and K-theory.

We will define vector bundles and give several examples of vector bundles that arise naturally in geometry. We will give constructions of important natural operations on vector bundles, and we will show how deformation of spaces controls the structure of vector bundles. In section 6.5 we will define K-theory, an important abelian invariant of a space. We will show that this invariant can be used to answer non-trivial questions about the geometry of a space. The second part gives a brief overview of the Chern-Weil theory in the context of vector bundles. The Chern-Weil theory is a vast topic which has been studied from various aspects.

In this short note we take the differential geometric approach. We start with smooth manifolds and affine connections and generalize the notion of connections and curvature to vector bundles with an aim to produce global invariants of vector bundles in terms of characteristic classes. We conclude with a few simple examples. This is a preview of subscription content, log in via an institution to check access. Unable to display preview. Download preview PDF.

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The Plan Is For This To Be A Fairly Short

Much Of This Material Is Already Well Covered In Other

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