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Related papers: Equivariant Morse theory and quantum integrability

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Lurie and Gepner--Meier each define equivariant cohomology theories, namely \emph{tempered cohomology} and \emph{equivariant elliptic cohomology}, respectively, using derived algebraic geometry. We construct a natural equivalence between…

Algebraic Topology · Mathematics 2025-02-19 Jack Morgan Davies

In this paper, we develop methods for calculating equivariant homology from equivariant Morse functions on a closed manifold with the action of a finite group. We show how to alter $G$-equivariant Morse functions to a stable one, where the…

Geometric Topology · Mathematics 2025-02-04 Erkao Bao , Tyler Lawson

This text is an introduction to equivariant cohomology, a classical tool for topological transformation groups, and to equivariant intersection theory, a much more recent topic initiated by D. Edidin and W. Graham. It is based on lectures…

Algebraic Geometry · Mathematics 2007-05-23 Michel Brion

Using an equivariant version of Connes' Thom Isomorphism,w}e prove that equivariant $K$-theory is invariant under strict deformation quantization for a compact Lie group action.

Operator Algebras · Mathematics 2013-10-07 Xiang Tang , Yi-Jun Yao

We generalize the Cohen-Jones-Segal construction to the Morse-Bott setting. In other words, we define framings for Morse-Bott analogues of flow categories and associate a stable homotopy type to this data. We use this to recover the stable…

Algebraic Topology · Mathematics 2024-03-07 Laurent Côté , Yusuf Barış Kartal

A system of functional equations relating the Euler characteristics of moduli spaces of stable representations of quivers and the Euler characteristics of (Hilbert scheme-type) framed versions of quiver moduli is derived. This is applied to…

Algebraic Geometry · Mathematics 2014-01-14 Markus Reineke

In this paper we first consider the Hamiltonian action of a compact connected Lie group on an $H$-twisted generalized complex manifold $M$. Given such an action, we define generalized equivariant cohomology and generalized equivariant…

Differential Geometry · Mathematics 2009-11-11 Yi Lin

We present a new method for the consistent construction of time-continuous coherent-state path integrals using the theory of half-form quantization. Through the inversion of the quantization procedure we construct a de-quantization map…

Quantum Physics · Physics 2020-06-25 P. Lykourgias , I. Lyris , A. I. Karanikas

We study the GKM theory for a equivariant stratified space having orbifold structures in tis successive quotients. Then, we introduce the notion of an \emph{almost simple polytope}, as well as a \emph{divisive toric variety} generalizing…

Algebraic Topology · Mathematics 2020-12-03 Soumen Sarkar , Jongbaek Song

The results of a previous paper on the equivariant homotopy theory of crossed complexes are generalised from the case of a discrete group to general topological groups. The principal new ingredient necessary for this is an analysis of…

Algebraic Topology · Mathematics 2016-08-15 R Brown , M Golasiński , T Porter , A Tonks

Let G be a compact, connected Lie group, acting smoothly on a manifold M. Goresky-Kottwitz-MacPherson described a small Cartan model for the equivariant cohomology of M, quasi-isomorphic to the standard Cartan complex of equivariant…

Differential Geometry · Mathematics 2007-07-26 A. Alekseev , E. Meinrenken

In the present paper we introduce and study the notion of an equivariant pretheory: basic examples include equivariant Chow groups, equivariant K-theory and equivariant algebraic cobordism. To extend this set of examples we define an…

Algebraic Geometry · Mathematics 2013-02-07 Stefan Gille , Kirill Zainoulline

Using the Witten deformation and localization algebra techniques, we compute the $G$-equivariant $K$-homology class of the de Rham operator on a proper cocompact $G$-spin manifold, where $G$ is an almost connected Lie group. By applying a…

Operator Algebras · Mathematics 2025-08-22 Hongzhi Liu , Hang Wang , Zijing Wang , Shaocong Xiang

In this article we review the Duistermaat-Heckman integration formula and the ensuing equivariant cohomology structure, in the finite dimensional case. In particular, we discuss the connection between equivariant cohomology and classical…

High Energy Physics - Theory · Physics 2008-02-03 T. Karki , A. J. Niemi

We show that the main theorem of Morse theory holds for a large class of functions on singular spaces. The function must satisfy certain conditions extending the usual requirements on a manifold that Condition C holds and the gradient flow…

Symplectic Geometry · Mathematics 2017-07-03 Graeme Wilkin

We study the integrability and the Bethe/Gauge correspondence of the Generalized Calogero-Moser system proposed by Berntson, Langmann and Lenells which we call the elliptic quadruple Calogero-Moser system (eqCM). We write down the Dunkl…

High Energy Physics - Theory · Physics 2024-06-21 Taro Kimura , Norton Lee

This article is a survey of recent work of the authors developing a new approach to quantization based on the equivariance with respect to some Lie group of symmetries. Examples are provided by conformal and projective differential…

Differential Geometry · Mathematics 2007-05-23 C. Duval , P. Lecomte , V. Ovsienko

Equivariant Ehrhart theory generalizes the study of lattice point enumeration to also account for the symmetries of a polytope under a linear group action. We present a catalogue of techniques with applications in this field, including…

Combinatorics · Mathematics 2022-05-13 Sophia Elia , Donghyun Kim , Mariel Supina

We generalize several comparison results between algebraic, semi-topological and topological K-theories to the equivariant case with respect to a finite group.

K-Theory and Homology · Mathematics 2013-08-21 Jeremiah Heller , Jens Hornbostel

In this article, we give Maurer-Cartan characterizations of equivariant Lie superalgebra structures. We introduce equivariant cohomology and equivariant formal deformation theory of Lie superalgebras. As an application of equivariant…

General Mathematics · Mathematics 2023-01-04 RB Yadav , Subir Mukhopadhyay