Special Issue "Algebraic K-Theory and Applications"
A special issue of Mathematics (ISSN 2227-7390).
Deadline for manuscript submissions: 31 May 2019
Algebraic K-theory is a discipline of mathematics with connections to geometry, topology, ring theory and number theory. Geometric, algebraic and arithmetic objects are assigned groups called K-groups. They contain detailed information about original object but are difficult to compute. For example, an important outstanding problem is to compute the K-groups of the integers. K-theory was invented in the late 1950s by Alexander Grothendieck in his study of intersection theory on algebraic varieties. Algebraic K-theory has two components: the classical theory which centers around the Grothendieck group of a category, and higher algebraic K-theory which requires topological or homological machinery to define. It is based on the fundamental works of Grothendieck, Bass, Milnor, Swan, Quillen and Waldhausen. There are four basic constructions for higher algebraic K-theory: the +–construction for rings, the group completion constructions for symmetric monoidal categories, Quillen’s Q-construction for exact categories, and Waldhausen’s wS. construction for categories with cofibrations and weak equivalences. All these constructions give the same K-theory of a ring, but are useful in various distinct settings. Algebraic K-theory is intensively developed worldwide as a fundamental area of mathematics (algebra, topology, geometry) and has important applications in algebraic topology and algebraic geometry.
We invite and welcome original research articles dealing with recent advances in algebraic K-theory and its applications.
Prof. Dr. Hvedri Inassaridze
Manuscript Submission Information
Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All papers will be peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.
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- projective module
- higher K-functor
- homotopy functor
- K-theory space
- simplicial group
- monoidal category
- vector bundle
- geometric realization