Topological K-Theory

Vector bundles, Bott periodicity, and index theorems.


field tier

Topological K-Theory. Vector bundles, Bott periodicity, and index theorems.

Foundations and canonical references

The standard treatments of topological k-theory approach the subject from complementary angles. Atiyah, K-Theory (1989) is the anchor reference for the subject and lays out the core definitions, theorems, and worked examples that practitioners return to. Hatcher, Vector Bundles and K-Theory (2009) gives a parallel, more proof-oriented exposition of the same material and is widely used as a graduate text.

Open methodological questions for topological k-theory include sharpening the bridges between foundational theory and computational practice, extending classical results to broader or more structured settings, and integrating the techniques surveyed above with adjacent mathematical disciplines. The references listed in this page are the entry points that current work builds on.

Prerequisites

Sources

  • textbook · primary · 1989
    K-Theory
    atiyah-1989
  • textbook · primary · 2009
    Vector Bundles and K-Theory
    hatcher-2009

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