19M05 Miscellaneous applications of $K$-theory

Overview

19M05 studies miscellaneous applications of $k$-theory in miscellaneous applications. It collects applications of K-theory that do not fit more specialized arithmetic, topological, or operator-algebraic categories.

Related Wikipedia Page

Miscellaneous Applications (Wikipedia)

Useful Links

• Miscellaneous Applications (Wikipedia)
• Algebraic K-theory (Wikipedia)
• Grothendieck group (Wikipedia)

Key Ideas

• Canonical formulations and representative examples for miscellaneous applications of $k$-theory
• How structural, local, and computational viewpoints interact in the subject
• Standard theorem patterns and invariants used in current research practice

Typical Uses

Used to organize cross-cutting applications of K-theory across geometry, topology, and algebra.

Applications

• Cross-disciplinary K-theory
• Comparative invariants
• Applications across algebra and topology

References

• Weibel, C.A. (2013) The K-book: An Introduction to Algebraic K-theory. Providence, RI: American Mathematical Society.
• Bass, H. (1968) Algebraic K-Theory. New York, NY: Benjamin.

Recommended Textbooks

• Rudin, W. (1976) Principles of Mathematical Analysis. 3rd edn. New York, NY: McGraw-Hill.
• Topic-focused textbook search (n.d.) Miscellaneous applications of K-theory. Available via Amazon search.