Algebraic K-theory is a subject area in mathematics with connections to geometry, topology, ring theory, and number theory. Geometric, algebraic, and arithmetic objects are assigned objects …

In this section, we discuss another fundamental technique in al-gebraic K-theory, known as localization, which essentially yields an excision exact sequence relating the K-theory of X and …

In 1985, I started hearing a persistent rumor that I was writing a book on algebraic K-theory. This was a complete surprise to me! After a few years, I had heard the rumor from at least a dozen …

Aug 7, 2010 · We present 18 Introductory Lectures on K-Theory covering its basic three branches, namely topological, analytic (K-Homology) and Higher Algebraic K-Theory, 6 lectures on each …

The story starts within algebraic geometry, when in 1957 Grothendieck de-ned K0 of an algebraic variety (which we now call the Grothendieck group of a variety) in order to prove a …

Algebraic K-Theory has become an increasingly active area of research. With its connections to algebra, algebraic geometry, topology, and number theory, it has implications for a wide …

K -theory groups For this chapter, we suppose known the notions of action, fundamental group, covering space, universal covering space, bration and co bration and the theorem of van …

Jan 10, 2015 · Algebraic $K$-theory makes extensive use of the theory of rings, homological algebra, category theory and the theory of linear groups. Algebraic $K$-theory has two …

Feb 18, 2025 · Algebraic K-theory is about natural constructions of cohomology theories / spectra from algebraic data such as commutative rings, symmetric monoidal categories and various …

This book is intended as an introduction to algebraic K-theory that can serve as a second-semester course in algebra. A first algebra course develops the basic structures of groups, …

This chapter will mainly be concerned with the algebraic K-theory of rings, but we will extend this notion at the end of the chapter. There are various possible extensions, but we will mostly …

Sep 12, 2015 · The multiplicative structure of algebraic K-theory makes KGL KGL into a ring spectrum (up to homotopy), which comes from a unique structure of E∞ E_\infty -algebra (see …

This text consists of unoficial notes on the lecture Advanced Topics in Algebra – Algebraic and Hermitian K-Theory, taught at the University of Bonn by Fabian Hebestreit in the winter term …

Algebraic K-theory is a modern branch of algebra which has many important applications in fundamental areas of mathematics connected with algebra, topology, algebraic geometry, …

For a general symmetric monoidal category S, we de ne the K-theory space of Sto be K(isoS). As usual, the K-groups of Sare simply the homotopy groups of the K-theory space.

Feb 18, 2025 · Algebraic K-theory is about natural constructions of cohomology theories / spectra from algebraic data such as commutative rings, symmetric monoidal categories and various …

I" Turns out it was di cult to prove the basic theorems of algebraic K-theory using the + construction. We might expect this from the ad hoc addition of K0(R), which is divorced from …

raic K-theory of rings and ge-ometry. This note is divided into four parts : Classical K-theory, Quillen’s higher K-theory, K-theory of brave new rings, and a short appendix collecting the few …

In mathematics, K-theory is, roughly speaking, the study of a ring generated by vector bundles over a topological space or scheme. In algebraic topology, it is a cohomology theory known as …

This survey contains many of the classical constructions and applications of topological Hochschild homology (THH), topological cyclic homology (TC), and the cyclotomic trace map …