Related papers: Lectures on Chow-Witt groups
We study the algebra of Wilson line operators in three-dimensional N=2 supersymmetric U(M) gauge theories with a Higgs phase related to a complex Grassmannian Gr(M,N), and its connection to K-theoretic Gromov-Witten invariants for Gr(M,N).…
Regular algebraic $K$-theory for groups is a homology theory for discrete groups closely connected (but different from) group homology. It also gives a version of algebraic $K$-theory for rings by the simple functorial mapping assigning to…
A Hom-group G is a nonassociative version of a group where associativity, invertibility, and unitality are twisted by a map \alpha: G\longrightarrow G. Introducing the Hom-group algebra KG, we observe that Hom-groups are providing examples…
This article presents two key computations in MW-motivic cohomology. Firstly, we compute the MW-motivic cohomology of the symplectic groups $Sp_{2n}$ for any $n\in\mathbb{N}$ using the $Sp$-orientation and the associated Borel classes.…
Hilbert--Lie groups are Lie groups whose Lie algebra is a real Hilbert space whose scalar product is invariant under the adjoint action. These infinite-dimensional Lie groups are the closest relatives to compact Lie groups. Here we study…
We give natural descriptions of the homology and cohomology algebras of regular quotient ring spectra of even E-infinity ring spectra. We show that the homology is a Clifford algebra with respect to a certain bilinear form naturally…
We extend the definitions and main properties of graded extensions to the category of locally compact groupoids endowed with involutions. We introduce Real \v{C}ech cohomology, which is an equivariant-like cohomology theory suitable for the…
In this article, we'll introduce a $q$-variant of Witt vectors and de Rham-Witt complexes. This variant is closely related to the Habiro ring of a number field constructed by Garoufalidis, Scholze, Wheeler, and Zagier, to $q$-Hodge…
This survey is based on my talk at the conference `Classical algebraic geometry today' at the MSRI. Some new results on the action of symplectomorphisms on the Chow group are added.
In this paper we analyse the topological group cohomology of finite-dimensional Lie groups. We introduce a technique for computing it (as abelian groups) for torus coefficients by the naturally associated long exact sequence. The upshot in…
The operational Chow cohomology classes of a complete toric variety are identified with certain functions, called Minkowski weights, on the corresponding fan. The natural product of Chow cohomology classes makes the Minkowski weights into a…
We extend our consideration of commutative subalgebras (rays) in different representations of the $W_{1+\infty}$ algebra to the elliptic Hall algebra (or, equivalently, to the Ding-Iohara-Miki (DIM) algebra…
Graphs with given k vertices generate an (acyclic) simplicial complex. We describe the homology of its quotient complex, formed by all connected graphs, and demonstrate its applications to the topology of braid groups, knot theory,…
Certain topologies on Milnor K-groups of higher local fields K are studied. These are related to the topology on the multiplicative group and important for explicit higher local class field theory. The structure of the quotient of Milnor…
We prove that structure constants related to Hecke algebras at roots of unity are special cases of k-Littlewood-Richardson coefficients associated to a product of k-Schur functions. As a consequence, both the 3-point Gromov-Witten…
We study the logarithmic topological Hochschild homology of ring spectra with logarithmic structures and establish localization sequences for this theory. Our results apply, for example, to connective covers of periodic ring spectra like…
We develop cohomological and homological theories for a profinite group $G$ with coefficients in the Pontryagin dual categories of pro-discrete and ind-profinite $G$-modules, respectively. The standard results of group (co)homology hold for…
Due to the work of many authors in the last decades, given an algebraic orbifold (smooth proper Deligne-Mumford stack with trivial generic stabilizer), one can construct its orbifold Chow ring and orbifold Grothendieck ring, and relate them…
In this article we give a characterisation of the Baum-Connes assembly map with coefficients. The technical tools needed are the K-theory of C*-categories, and equivariant KK-theory in the world of groupoids.
Given a unital action $\theta $ of an inverse monoid $S$ on an algebra $A$ over a filed $K$ we produce (co)homology spectral sequences which converge to the Hochschild (co)homology of the crossed product $A\rtimes_\theta S$ with values in a…