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Gauge theory and knot homologies

✍ Scribed by S. Gukov

Publisher
John Wiley and Sons
Year
2007
Tongue
English
Weight
301 KB
Volume
55
Category
Article
ISSN
0015-8208

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✦ Synopsis

Abstract

Topological gauge theories in four dimensions which admit surface operators provide a natural framework for realizing homological knot invariants. Every such theory leads to an action of the braid group on branes on the corresponding moduli space. This action plays a key role in the construction of homological knot invariants. We illustrate the general construction with a simple example based on surface operators in 𝒩 = 4 twisted gauge theory which lead to a categorification of a variant of the Casson invariant.

πŸ“œ SIMILAR VOLUMES

Novikov homologies in Knot theory
Novikov homologies in Knot theory
✍ A. Yu. Lazarev πŸ“‚ Article πŸ“… 1992 πŸ› SP MAIK Nauka/Interperiodica 🌐 English βš– 343 KB
Casson's knot invariant and gauge theory
Casson's knot invariant and gauge theory
✍ K. Masataka πŸ“‚ Article πŸ“… 2001 πŸ› Elsevier Science 🌐 English βš– 250 KB

It is known that twice the Casson invariant for integral homology 3 spheres is equal to the Euler characteristic of the Floer homology group of them. Here we show that a similar result holds in case of the Casson invariant for knots in integral homology 3 spheres. This result is obtained as a coroll