Symplectic instanton homology: naturality, and maps from cobordisms

IF 1 2区数学 Q1 MATHEMATICS

Quantum Topology Pub Date : 2017-10-11 DOI:10.4171/qt/129

Guillem Cazassus

引用次数: 4

Abstract

We prove that Manolescu and Woodward's Symplectic Instanton homology, and its twisted versions are natural, and define maps associated to four dimensional cobordisms within this theory. This allows one to define representations of the mapping class group and the fundamental group of a 3-manifold, and to have a geometric interpretation of the maps appearing in the long exact sequence for symplectic instanton homology, together with vanishing criterions.

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辛瞬子同调:自然性，和从协点映射

我们证明了Manolescu和Woodward的辛瞬子同调及其扭曲版本是自然的，并在该理论中定义了与四维配合相关的映射。这允许人们定义映射类群和3流形的基本群的表示，并对出现在辛瞬时同调的长精确序列中的映射以及消失准则进行几何解释。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Quantum Topology Mathematics-Geometry and Topology

CiteScore

1.80

自引率

9.10%

发文量

期刊介绍： Quantum Topology is a peer reviewed journal dedicated to publishing original research articles, short communications, and surveys in quantum topology and related areas of mathematics. Topics covered include in particular: Low-dimensional Topology Knot Theory Jones Polynomial and Khovanov Homology Topological Quantum Field Theory Quantum Groups and Hopf Algebras Mapping Class Groups and Teichmüller space Categorification Braid Groups and Braided Categories Fusion Categories Subfactors and Planar Algebras Contact and Symplectic Topology Topological Methods in Physics.