Related papers: A Quick Overview On Regular Algebraic K-Theory For…
The chapter provides an introduction to the basic concepts of Algebraic Topology with an emphasis on motivation from applications in the physical sciences. It finishes with a brief review of computational work in algebraic topology,…
The paper begins by exploring the various definitions of norms on semigroups and then presents a new definition of a normed semigroup. The properties of normed semigroups in the new sense are investigated. The new definition of the norm is…
A group equivariant $KK$-theory for rings will be defined and studied in analogy to Kasparov's $KK$-theory for $C^*$-algebras. It is a kind of linearization of the category of rings by allowing addition of homomorphisms, imposing also…
We give formulas for the Whitehead groups and the rational $K$-theory groups of the (integer group ring of the) Hilbert modular group in terms of its maximal finite subgroups.
We introduce the notions of relational groupoids and relational convolution algebras. We provide various examples arising from the group algebra of a group $G$ and a given normal subgroup $H$. We also give conditions for the existence of a…
We introduce a global equivariant refinement of algebraic K-theory; here `global equivariant' refers to simultaneous and compatible actions of all finite groups. Our construction turns a specific kind of categorical input data into a global…
This is an overview of results from our experiment of merging two seemingly unrelated disciplines - higher algebraic K-theory of rings and the theory of lattice polytopes. The usual K-theory is the ``theory of a unit simplex''. A conjecture…
We view strict ring spectra as generalized rings. The study of their algebraic K-theory is motivated by its applications to the automorphism groups of compact manifolds. Partial calculations of algebraic K-theory for the sphere spectrum are…
This note consists of three unrelated remarks. First, we demonstrate how roughly speaking $*$-homomorphisms between matrix stable $C^*$-algebras are exactly the uniformly continuous $*$-preserving group homomorphisms between their genral…
In this paper we define complex equivariant K-theory for actions of Lie groupoids using finite-dimensional vector bundles. For a Bredon-compatible Lie groupoid, this defines a periodic cohomology theory on the category of finite equivariant…
We compute the first two symplectic quadratic K-theory groups of the integers, or equivalently, the first two stable homology groups of the group of symplectic integral matrices preserving the standard quadratic refinement. The main novelty…
We introduce and study a $K$-theory of twisted bundles for associative algebras $A(\mathfrak g)$ of formal series with an infinite-Lie algebra coefficients over arbitrary compact topological spaces. Fibers of such bundles are given by…
In this talk we introduce several topics in combinatorial number theory which are related to groups; the topics include combinatorial aspects of covers of groups by cosets, and also restricted sumsets and zero-sum problems on abelian…
We develop some basic homological theory of hopfological algebra as defined by Khovanov. Several homological properties in hopfological algebra analogous to those of usual homological theory of DG algebras are obtained.
We study the K-theory of actions of diagonalizable group schemes on noetherian regular separated algebraic spaces: our main result shows how to reconstruct the K-theory ring of such an action from the K-theory rings of the loci where the…
We introduce a general class of Heisenberg groups motivated by applications of algebraic Fourier theory. Basic properties are examined from a homological perspective.
This is an introduction to the basic ideas and to a few further selected topics in conformal quantum field theory and in the theory of Kac-Moody algebras.
We provide descriptions of the Whitehead groups, and the algebraic $K$-theory groups, of the fundamental group of a connected, oriented, closed $3$-manifold in terms of Whitehead groups of their finite subgroups and certain Nil-groups. The…
The goal of this paper is to prove the Riemann-Roch isomorphism for the higher equivariant K-theory of varieties with action of a linear algebraic group.
In topology there is a theorem of Atiyah, concerning K-theory of classifying space of connected compact Lie group. We consider an algebraic analogue of this theorem. We prove that for a split reductive algebraic group G over a field there…