Related papers: A Localization Principle for Orbifold Theories

Gromov, in his seminal 1989 paper on the Oka principle, introduced the notion of an elliptic manifold and proved that every continuous map from a Stein manifold to an elliptic manifold is homotopic to a holomorphic map. We show that a much…

These are slightly informal lecture notes intended for graduate students about the standard local theory of holomorphic foliations and vector fields. Though the material presented here is well-known some of the proofs differs slightly from…

An equivariant topological field theory is defined on a cobordism category of manifolds with principal fiber bundles for a fixed (finite) structure group. We provide a geometric construction which for any given morphism $G \to H$ of finite…

In this paper, we develop twisted $K$-theory for stacks, where the twisted class is given by an $S^1$-gerbe over the stack. General properties, including the Mayer-Vietoris property, Bott periodicity, and the product structure $K^i_\alpha…

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 physical basis of the standard theory of general relativity is examined and a nonlocal theory of accelerated observers is described that involves a natural generalization of the hypothesis of locality. The nonlocal theory is confronted…

We introduce the notion of an E_k-ring with prelogarithmic structure, define logarithmic topological Hochschild homology and logarithmic topological cyclic homology in this context, and establish localization sequences for these theories.…

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 establish a localization theorem of Borel-Atiyah-Segal type for the equivariant operational K-theory of Anderson and Payne. Inspired by the work of Chang-Skjelbred and Goresky-Kottwitz-MacPherson, we establish a general form of GKM…

A foliation on a manifold M can be informally thought of as a partition of M into injectively immersed submanifolds, called leaves. In this thesis we study foliations whose leaves carry some specific geometric structures. The thesis…

Let $K$ be a number field and let $E/K$ be an elliptic curve whose mod $\ell$ Galois representation locally has image contained in a group $G$, up to conjugacy. We classify the possible images for the global Galois representation in the…

Various theories of spinning particles are interpreted as realizing elements of an underlying geometric theory. Classical particles are described by trajectories on the Poincare group. Upon quantization an eleven-dimensional Kaluza-Klein…

In this expository article, we give the foundations, basic facts, and first examples of unstable motivic homotopy theory with a view towards the approach of Asok-Fasel to the classification of vector bundles on smooth complex affine…

We give a purely cubical argument for the localization theorem for the cubical version of higher Chow groups.

It seems that the index theory for non-compact spaces has found its ultimate formulation in realm of coarse spaces and $K$-theory of related operator algebras. Relative and partitioned index theorems may be mentioned as two important and…

We study localizations of infinity categories that remain localizations after any base change.

We introduce $(k,l)$-regular maps, which generalize two previously studied classes of maps: affinely $k$-regular maps and totally skew embeddings. We exhibit some explicit examples and obtain bounds on the least dimension of a Euclidean…

We discuss orbifold version of the Schur index defined as the supersymmetric partition function in S^3/Z_n x S^1. We first give a general formula for Lagrangian theories obtained by localization technique, and then suggest a generalization…

We develop a mathematical framework for the computation of open orbifold Gromov-Witten invariants of [C^3/Z_n], and provide extensive checks with predictions from open string mirror symmetry. To this aim we set up a computation of open…

We construct a theory of particles moving in curved both momentum space and spacetime, being a generalization of Relative Locality. We find that in order to construct such theory, with desired symmetries, including the general coordinate…