Special Issue "Algebraic K-Theory and Applications"

A special issue of Mathematics (ISSN 2227-7390).

Deadline for manuscript submissions: 31 May 2019

Special Issue Editor

Guest Editor
Prof. Dr. Hvedri Inassaridze

A. Razmadze Mathematical Institute of Tbilisi State University, 6, Tamarashvili Str., Tbilisi 0177, Georgia
Website | E-Mail
Interests: K-theory; homotopical algebra; category theory; non-commutaive geometry

Special Issue Information

Dear Colleagues,

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
Guest Editor

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.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Mathematics is an international peer-reviewed open access monthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 850 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • projective module
  • higher K-functor
  • homotopy functor
  • K-theory space
  • Resolution
  • simplicial group
  • localization
  • monoidal category
  • vector bundle
  • geometric realization

Published Papers

This special issue is now open for submission.
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