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We use a variation of a classical construction of A. Hatcher to construct virtually all stable exotic smooth structures on compact smooth manifold bundles whose fibers have sufficiently large odd dimension (at least twice the base dimension…
In this note we point out that a symmetric product orbifold CFT can be twisted by a unique nontrivial two-cocycle of the permutation group. This discrete torsion changes the spins and statistics of corresponding second-quantized string…
We introduce equivariant twisted cohomology of a simplicial set equipped with simplicial action of a discrete group and prove that for suitable twisting function induced from a given equivariant local coefficients, the simplicial version of…
Suppose that a finite group $G$ acts on a smooth complex variety $X$. Then this action lifts to the Chiral de Rham Complex of $X$ and to its cohomology by automorphisms of the vertex algebra structure. We define twisted sectors for the…
We define the singular orbifold elliptic genus and $E$-function for all normal surfaces without strictly log-canonical singularities, and prove the analogue of the McKay correspondence in this setting. Our invariants generalize the stringy…
We present a classification theorem for closed smooth spin 2-connected 7-manifolds M. This builds on the almost-smooth classification from the first author's thesis. The main additional ingredient is an extension of the Eells-Kuiper…
We show the compatibility of the differential geometric and the topological construction of equivariant characteristic classes for compact Lie groups. Our analysis motivates a differential geometric construction for equivariant…
The elliptic genera of two-dimensional N=2 superconformal field theories can be twisted by the action of the integral Heisenberg group if their U(1) charges are fractional. The basic properties of the resulting twisted elliptic genera and…
A particular case of Bergeron-Venkatesh's conjecture predicts that torsion classes in the cohomology of Shimura varieties are rather rare. According to this and for Kottwitz-Harris-Taylor type of Shimura varieties, we first associate to…
We investigate group actions on the category of coherent sheaves over weighted projective lines. We show that the equivariant category with respect to certain finite group action is equivalent to the category of coherent sheaves over a…
We introduce the notion of equivariant basic cohomology for singular Riemannian foliations with transverse infinitesimal actions, and prove some elementary properties such as its invariance under homotopies. For the particular case of…
Without recourse to the sophisticated machinery of twisted group algebras, projective character tables and explicit values of 2-cocycles, we here present a simple algorithm to study the gauge theory data of D-brane probes on a generic…
A kind of two-variable elliptic genus for almost-complex manifolds was introduced by Ping Li and its various properties were established by him. In this paper, we define a two-variable elliptic genus for odd dimensional spin manifolds which…
We construct differential equivariant K-theory of representable smooth orbifolds as a ring valued functor with the usual properties of a differential extension of a cohomology theory. For proper submersions (with smooth fibres) we construct…
In this paper we give a geometric construction of the Borel equivariant (co)homology for spaces with a $G$-action, where $G$ is a compact Lie group with the property that the adjoint representation is orientable. A nice feature of these…
This study introduces a new unified structural framework for orbifold sigma models that incorporates twisted sectors, singularities, and smooth regions into a single algebraic object. Traditional approaches to orbifold theories often treat…
For a compact Lie group acting on a smooth manifold, we define the differential cohomology of a certain quotient stack involving principal bundles with connection. This produces differential equivariant cohomology groups that map to the…
For a discrete group $\Gamma$ satisfying some finiteness conditions we give a Bredon projective resolution of the trivial module in terms of projective covers of the chain complex associated to certain posets of subgroups. We use this to…
The elliptic genus (EG) of a compact complex manifold was introduced as a holomorphic Euler characteristic of some formal power series with vector bundle coefficients. EG is an automorphic form in two variables only if the manifold is a…
The article presents four reasons why the elliptic genus is the most general characteristic class that admits a generalization to singular spaces. We prove that the elliptic characteristic class (with an additional factor) is essentially…