相关论文: A loop group extension of the odd Chern character

We define an extended Bloch group and show it is naturally isomorphic to H_3(PSL(2,C)^\delta ;Z). Using the Rogers dilogarithm function this leads to an exact simplicial formula for the universal Cheeger-Chern-Simons class on this homology…

The Chern character maps are one of the most important working tools in mathematics. Although they admit numerous different constructions, they are not yet fully understood at the conceptual level. In this note we eliminate this gap by…

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…

We study the existence of $S^1$-equivariant characteristic classes on certain natural infinite rank bundles over the loop space $LM$ of a manifold $M$. We discuss the different $S^1$-equivariant cohomology theories in the literature and…

We observe that linear relations among Chern-Mather classes of projective varieties are preserved by projective duality. We deduce the existence of an explicit involution on a part of the Chow group of projective space, encoding the effect…

We extend the Chern character on K-theory, in its generalization to the Chern-Dold character on generalized cohomology theories, further to (twisted, differential) non-abelian cohomology theories, where its target is a non-abelian de Rham…

Using similarities between topological $K$-theory and periodic cyclic homology we show that, after tensoring with $\mathbb C$, for certain Fr\'echet algebras the Chern character provides an isomorphism between these functors. This is…

In this note, we answer the questions "What does Chern-Simons theory assign to a point?" and "What kind of mathematical object does Chern-Simons theory assign to a point?". Our answer to the first question is representations of the based…

We prove an identity relating the product of two opposite Schubert varieties in the (equivariant) quantum K-theory ring of a cominuscule flag variety to the minimal degree of a rational curve connecting the Schubert varieties. We deduce…

We study the nonrelativistic limit of the $N=2$ supersymmetric Chern-Simons matter system. We show that in addition to Galilean invariance the model admits a set of symmetries generated by fermionic charges, which can be interpreted as an…

We construct a groupoid equivariant Kasparov class for transversely oriented foliations in all codimensions. In codimension 1 we show that the Chern character of an associated semifinite spectral triple recovers the Connes-Moscovici cyclic…

For every finite dimensional Lie group one can consider the group of all smooth loops on it, called its loop group. Such loop groups have long been studied for, among other reasons, their relations to conformal field theories and…

We give a description of the delocalized twisted cohomology of an orbifold and the Chern character of a twisted vector bundle in terms of supersymmetric Euclidean field theories. This includes the construction of a twist functor for…

In this paper, I construct noncompact analogs of the Chern classes of equivariant vector bundles over complex reductive groups. For the tangent bundle, these Chern classes yield an adjunction formula for the Euler characteristic of complete…

Non-abelian Chern-Simons theories coupled to fermions are known to provide an interesting class of non-supersymmetric conformal fixed points \cite{Giombi:2011kc}. These theories, particularly those based on bifundamental matter, are…

We unify problems about the equivariant geometry of symmetric quiver representation varieties, in the finite type setting, with the corresponding problems for symmetric varieties $GL(n)/K$ where $K$ is an orthogonal or symplectic group. In…

We establish several Witten type rigidity and vanishing theorems for twisted Toeplitz operators on odd dimensional manifolds. We obtain our results by combining the modular method, modular transgression and some careful analysis of odd…

Using the Wodzicki residue, we build Wodzicki-Chern-Simons (WCS) classes in $H^{2k-1}(LM)$ associated to the residue Chern character on the loop space $LM$ of a Riemannian manifold $M^{2k-1}$. These WCS classes are associated to the $L^2$…

We construct toral Chern-Simons theory with gauge group $\mathbb T=\mathfrak t/\Lambda\cong U(1)^n$ from an even, integral, nondegenerate symmetric bilinear form $K:\Lambda\times\Lambda\to\mathbb Z$ by geometric quantization via real…

By a theorem of Bernhard Keller the de Rham cohomology of a smooth variety is isomorphic to the periodic cyclic homology of the differential graded category of perfect complexes on the variety. Both the de Rham cohomology and the cyclic…