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Algebraic K-Theory
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, functional analysis and algebraic number theory. Methods of algebraic K-theory are actively used in algebra and related fields, achieving interesting results. This book presents the elements of algebraic K-theory, based essentially on the fundamental works of Milnor, Swan, Bass, Quillen, Karoubi, Gersten, Loday and Waldhausen. It includes all principal algebraic K-theories, connections with topological K-theory and cyclic homology, applications to the theory of monoid and polynomial algebras and in the theory of normed algebras. This volume will be of interest to graduate students and research mathematicians who want to learn more about K-theory.
Non-Abelian Homological Algebra and Its Applications
This book exposes methods of non-abelian homological algebra, such as the theory of satellites in abstract categories with respect to presheaves of categories and the theory of non-abelian derived functors of group valued functors. Applications to K-theory, bivariant K-theory and non-abelian homology of groups are given. The cohomology of algebraic theories and monoids are also investigated. The work is based on the recent work of the researchers at the A. Razmadze Mathematical Institute in Tbilisi, Georgia. Audience: This volume will be of interest to graduate students and researchers whose work involves category theory, homological algebra, algebraic K-theory, associative rings and algebras; algebraic topology, and algebraic geometry.
Journal of Homotopy and Related Structures 5(1)
Homotopy is a basic discipline of mathematics having fundamental and various applications to important fields of mathematics. The Journal has a wide scope which ranges from homotopical algebra and algebraic number theory and functional analysis. Diverse algebraic, geometric, topological and categorical structures are closely related to homotopy and the influence of homotopy is found in many fundamental areas of mathematics such as general algebra, algebraic topology, algebraic geometry, category theory, differential geometry, computer science, K-theory, functional analysis, Galois theory ad in physical sciences as well. The J. Homotopy and Related Structures intends to develop its vision on the determining role of homotopy in mathematics. the aim of the Journal is to show the importance, merit and diversity of homotopy in mathematical sciences. The J. Homotopy and Related structures is primarily concerned with publishing carefully refereed significant and original research papers. However a limited number of carefully selected survey and expository papers are also included, and special issues devoted to Proceedings of meetings in the field as well as to Festschrifts.
Journal of Homotopy and Related Structures 6(1&2)
Homotopy is a basic discipline of mathematics having fundamental and various applications to important fields of mathematics. The Journal has a wide scope which ranges from homotopical algebra and algebraic number theory and functional analysis. Diverse algebraic, geometric, topological and categorical structures are closely related to homotopy and the influence of homotopy is found in many fundamental areas of mathematics such as general algebra, algebraic topology, algebraic geometry, category theory, differential geometry, computer science, K-theory, functional analysis, Galois theory ad in physical sciences as well. The J. Homotopy and Related Structures intends to develop its vision on the determining role of homotopy in mathematics. the aim of the Journal is to show the importance, merit and diversity of homotopy in mathematical sciences. The J. Homotopy and Related structures is primarily concerned with publishing carefully refereed significant and original research papers. However a limited number of carefully selected survey and expository papers are also included, and special issues devoted to Proceedings of meetings in the field as well as to Festschrifts.
Tbilisi - Mathematics
The Special Issues of Tbilisi Mathematical Journal are fully refereed international publications, publishing original research papers in all areas of pure and applied mathematics. The editors are well known experts in the field, particularly from leading universities of USA and Europe. Papers should satisfy high standards and only works of high quality are recommended for publication. They constitute a collection around selected themes related to mathematical sciences, or coming from a specific group of mathematicians or event, or coming from a workshop, symposia and international mathematical conferences.
Equivariant Homology and Cohomology of Groups
We provide and study an equivariant theory of group (co)homology of a group with coefficients in a ¡-equivariant -module , when a separate group ¡ acts on and , generalizing the classical Eilenberg-MacLane (co)homology theory of groups. Relationship with equivariant cohomology of topological spaces is established and application to algebraic -theory is given.
Tbilisi Mathematical Journal
Tbilisi Mathematical Journal (TMJ) is a fully refereed international journal, publishing original research papers in all areas of mathematics. Papers should satisfy the high standards and only works of high quality will be recommended for publication. The Management Committee may occasionally decide to invite the submission of survey and expository papers of the highest quality. Unsolicited submissions of survey and expository papers will not be considered for publication. Volume 3 (2010) contains two research papers by outstanding mathematicians.
