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Related papers: Applications of equivariant factorization homology

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In this paper, we study the equivariant homotopy type of a connected sum of linear actions on complex projective planes defined by Hambleton and Tanase. These actions are constructed for cyclic groups of odd order. We construct cellular…

Algebraic Topology · Mathematics 2021-09-28 Samik Basu , Pinka Dey , Aparajita Karmakar

We introduce a new cohomology theory for stacks called elliptic Hochschild homology, prove some fundamental properties and compute it in some classes of examples. We then introduce its periodic cyclic version and show that, over the complex…

Algebraic Geometry · Mathematics 2023-09-18 Nicolò Sibilla , Paolo Tomasini

We introduce an equivariant version of Hochschild cohomology as the deformation cohomology to study equivariant deformations of associative algebras equipped with finite group actions.

Rings and Algebras · Mathematics 2018-04-17 Goutam Mukherjee , Raj Bhawan Yadav

Univalent homotopy type theory (HoTT) may be seen as a language for the category of $\infty$-groupoids. It is being developed as a new foundation for mathematics and as an internal language for (elementary) higher toposes. We develop the…

Category Theory · Mathematics 2023-06-22 Egbert Rijke , Michael Shulman , Bas Spitters

The cohomology of a tiling or a point pattern has originally been defined via the construction of the hull or the groupoid associated with the tiling or the pattern. Here we present a construction which is more direct and therefore easier…

Mathematical Physics · Physics 2009-11-07 Johannes Kellendonk

We show injectivity results for assembly maps using equivariant coarse homology theories with transfers. Our method is based on the descent principle and applies to a large class of linear groups or, more general, groups with finite…

K-Theory and Homology · Mathematics 2021-05-28 Ulrich Bunke , Alexander Engel , Daniel Kasprowski , Christoph Winges

We introduce the study of parametrized higher category theory and parametrized higher algebra, and we describe the main theorems of the series of Expos\'es that make up the monograph.

Algebraic Topology · Mathematics 2016-08-15 Clark Barwick , Emanuele Dotto , Saul Glasman , Denis Nardin , Jay Shah

We use the periodicity properties of generalized Gauss sums to factor numbers. Moreover, we derive rules for finding the factors and illustrate this factorization scheme for various examples. This algorithm relies solely on interference and…

Quantum Physics · Physics 2012-10-25 S. Wölk , W. Merkel , W. P. Schleich , I. Sh. Averbukh , B. Girard

We construct a genuine $G$-equivariant extension of factorization homology for $G$ a finite group, assigning a genuine $G$-spectrum to a manifold with $G$-action. We show that $G$-factorization homology is compatible with…

Algebraic Topology · Mathematics 2019-10-17 Asaf Horev

In this note we prove an equivariant version of a result of Cartan for equivariant simplicial cohomology with local coefficients.

Algebraic Topology · Mathematics 2010-03-19 Debasis Sen

These are notes from an informal mini-course on factorization homology, infinity-categories, and topological field theories. The target audience was imagined to be graduate students who are not homotopy theorists.

Algebraic Topology · Mathematics 2020-10-07 Araminta Amabel , Artem Kalmykov , Lukas Müller , Hiro Lee Tanaka

Mott noted a one-to-one correspondence between saturated multiplicatively closed subsets of a domain D and directed convex subgroups of the group of divisibility D. With this, we construct a functor between inclusions into saturated…

Commutative Algebra · Mathematics 2016-12-15 Jim Coykendall , Brandon Goodell

For each positive integer n the HOMFLY polynomial of links specializes to a one-variable polynomial that can be recovered from the representation theory of quantum sl(n). For each such n we build a doubly-graded homology theory of links…

Quantum Algebra · Mathematics 2007-05-23 Mikhail Khovanov , Lev Rozansky

We will discuss the equivariant cohomology of a manifold endowed with the action of a Lie group. Localization formulae for equivariant integrals are explained by a vanishing theorem for equivariant cohomology with generalized coefficients.…

Differential Geometry · Mathematics 2007-05-23 Michele Vergne

This is an expository paper discussing various versions of Khovanov homology theories, interrelations between them, their properties, and their applications to other areas of knot theory and low-dimensional topology.

Geometric Topology · Mathematics 2011-01-31 Alexander Shumakovitch

We relativise double categories of relations to stable orthogonal factorisation systems. Furthermore, we present the characterisation of the relative double categories of relations in two ways. The first utilises a generalised comprehension…

Category Theory · Mathematics 2025-01-24 Keisuke Hoshino , Hayato Nasu

In group representations several inductions given by tensoring with appropriate bimodules may be reconstructed via homology of $G$-posets with $G$-equivariant coefficients. For this purpose, we need various local categories of a finite…

Representation Theory · Mathematics 2018-10-23 Fei Xu

We define the equivariant holonomy of an invariant connection on a principal U(1)-bundle. The properties of the ordinary holonomy are generalized to the equivariant setting. In particular, equivariant U(1)-bundles with connection are shown…

Differential Geometry · Mathematics 2019-07-02 Roberto Ferreiro Perez

We study equivariant coarse homology theories through an axiomatic framework. To this end we introduce the category of equivariant bornological coarse spaces and construct the universal equivariant coarse homology theory with values in the…

K-Theory and Homology · Mathematics 2021-05-28 Ulrich Bunke , Alexander Engel , Daniel Kasprowski , Christoph Winges

We want to construct a homological link invariant whose Euler characteristic is MOY polynomial as Khovanov and Rozansky constructed a categorification of HOMFLY polynomial. The present paper gives the first step to construct a…

Quantum Algebra · Mathematics 2008-07-01 Yasuyoshi Yonezawa