## Geometry And Topology Seminar - Aliakbar Daemi - Lagrangians, SO(3)-instantons and the Atiyah-Floer Conjecture

- Calendar
- Mathematics & Statistics

- Date
- 11.11.2021 3:30 pm - 4:30 pm

### Description

Speaker: Aliakbar Daemi (Washington University in St. Louis)

Title: Lagrangians, SO(3)-instantons and the Atiyah-Floer Conjecture

Abstract: A useful tool to study a 3-manifold is the space of the representations of its fundamental group, a.k.a. the 3-manifold group, into a Lie group. Any 3-manifold can be decomposed as the union of two handlebodies. Thus, representations of the 3-manifold group into a Lie group can be obtained by intersecting representation varieties of the two handlebodies. Casson utilized this observation to define his celebrated invariant. Later Taubes introduced an alternative approach to define Casson invariant using more geometric objects. By building on Taubes' work, Floer refined Casson invariant into a graded vector space whose Euler characteristic is twice the Casson invariant. The Atiyah-Floer conjecture states that Casson's original approach can be also used to define a graded vector space and the resulting invariant of 3-manifolds is isomorphic to Floer's theory. In this talk, after giving some background, I will discuss some recent progress on the Atiyah-Floer conjecture for SO(3) bundles, which is based on a joint work with Kenji Fukaya and Maksim Lipyanskyi. I will only assume a basic background in algebraic topology and geometry.

Title: Lagrangians, SO(3)-instantons and the Atiyah-Floer Conjecture

Abstract: A useful tool to study a 3-manifold is the space of the representations of its fundamental group, a.k.a. the 3-manifold group, into a Lie group. Any 3-manifold can be decomposed as the union of two handlebodies. Thus, representations of the 3-manifold group into a Lie group can be obtained by intersecting representation varieties of the two handlebodies. Casson utilized this observation to define his celebrated invariant. Later Taubes introduced an alternative approach to define Casson invariant using more geometric objects. By building on Taubes' work, Floer refined Casson invariant into a graded vector space whose Euler characteristic is twice the Casson invariant. The Atiyah-Floer conjecture states that Casson's original approach can be also used to define a graded vector space and the resulting invariant of 3-manifolds is isomorphic to Floer's theory. In this talk, after giving some background, I will discuss some recent progress on the Atiyah-Floer conjecture for SO(3) bundles, which is based on a joint work with Kenji Fukaya and Maksim Lipyanskyi. I will only assume a basic background in algebraic topology and geometry.

https://mcmaster.zoom.us/j/93187607131?pwd=OEhjbFBSMHZIUXF1a1BxT3VhL3cxQT09

ID: 931 8760 7131

Pass: Second word in Geometry & Topology

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