Casson invariants via virtual counting
Junwu Tu
TL;DR
This paper introduces a new way to define Casson invariants using virtual counting methods and proposes a general framework for deriving invariants from Chern-Simons gauge theories via derived differential geometry.
Contribution
It presents an alternative definition of Casson invariants through virtual counting and introduces a framework for invariants from Chern-Simons theories using derived geometry.
Findings
New definition of Casson invariants via virtual counting
Framework for invariants from Chern-Simons gauge theories
Application of derived differential geometry in gauge theory
Abstract
This is a research announcement on an alternative definition of the Casson invariants by means of virtual counting of the moduli space of irreducible representations of the fundamental group into . Along the way, by using derived differential geometry, we propose a general framework to obtain invariants from Chern-Simons type gauge theories.
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Taxonomy
TopicsBlack Holes and Theoretical Physics · Homotopy and Cohomology in Algebraic Topology · Algebraic Geometry and Number Theory