相关论文: A Localization Principle for Orbifold Theories

The "fundamental theorem" for algebraic $K$-theory expresses the $K$-groups of a Laurent polynomial ring $L[t,t^{-1}]$ as a direct sum of two copies of the $K$-groups of $L$ (with a degree shift in one copy), and certain "nil" groups of…

We introduce some general and special formulations of general position theorem for parametrized families of fractals and explain the techniques of its application to prove the existence of self-similar sets with prescribed special…

Formulae for the number of branch points of one-dimensional orbifolds defined over a non-archimedean local field and uniformisable by discrete projective linear groups are given. They depend only on the uniformising group. The method of…

We propose a notion of 1-homotopy for generalized maps. This notion generalizes those of natural transformation and ordinary homotopy for functors. The 1-homotopy type of a Lie groupoid is shown to be invariant under Morita equivalence. As…

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…

We show a classification method for finite groupoids and discuss the cardinality of cosets and its relation with the index. We prove a generalization of the Lagrange's Theorem and establish a Sylow theory for groupoids.

We define several versions of a class of varieties $X_{\mathfrak{g}}$ attached to a complex reductive Lie algebra $\mathfrak{g}$, generalizing the Hilbert scheme of points on the plane. These include trigonometric and elliptic versions…

Quantization, at least in some formulations, involves replacing some algebra of observables by a (more non-commutative) deformed algebra. In view of the fundamental role played by K-theory in non-commutative geometry and topology, it is of…

In the present paper we discuss some recent versions of localisation methods for calculations in the groups of points of algebraic-like and classical-like groups. Namely, we describe relative localisation, universal localisation, and…

We establish Thom's jet transversality theorem for regular maps from an affine algebraic manifold to an algebraic manifold satisfying a suitable flexibility condition. It can be considered as the algebraic version of Forstneri\v{c}'s jet…

The aim of this article is to give a rather extensive, and yet nontechnical, account of the birth of the regularity theory for generalized minimal surfaces, of its various ramifications along the decades, of the most recent developments,…

Given a small category C, we show that there is a universal way of expanding C into a model category, essentially by formally adjoining homotopy colimits. The technique of localization becomes a method for imposing `relations' into these…

The theory of indices of Morse--Bott vector fields on a manifold is constructed and the famous localization problem for the transfer map is solved on its base in the present paper. As a consequence, we obtained addition theorems for the…

Localization methods are ubiquitous in cyclic homology theory, but vary in detail and are used in different scenarios. In this paper we will elaborate on a common feature of localization methods in noncommutative geometry, namely…

We describe a general construction providing index theorems localizing the Chern classes of the normal bundle of a subvariety inside a complex manifold. As particular instances of our construction we recover both Lehmann-Suwa's…

The physical concept of locality is first analyzed in the special relativistic quantum regime, and compared with that of microcausality and the local commutativity of quantum fields. Its extrapolation to quantum general relativity on…

We develop a theory of umkehr maps for twisted generalized homology theories. In this theory, interesting umkehr maps, including generalizations of important classical ones, are induced by cartesian morphisms of a certain category opfibred…

We prove very general index formulae for integral Galois modules, specifically for units in rings of integers of number fields, for higher K-groups of rings of integers, and for Mordell-Weil groups of elliptic curves over number fields.…

In this paper we prove a $K$-homology index theorem for the Toeplitz operators obtained from the multishifts of the Bergman space on several classes of egg-like domains. This generalizes our theorem with Douglas and Yu on the unit ball.

A family of fractal arrangements of circles is introduced for each imaginary quadratic field $K$. Collectively, these arrangements contain (up to an affine transformation) every set of circles in the extended complex plane with integral…