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An SU(3) variant of instanton homology for webs

Presented by: 
Peter Kronheimer Harvard University
Date: 
Thursday 17th August 2017 - 10:00 to 11:00
Venue: 
INI Seminar Room 1
Abstract: 
Let K be a trivalent graph embedded in 3-space (a web). In an earlier talk at this conference, Tom Mrowka outlined how one may define an instanton homology J(K) using gauge theory with structure group SO(3). This invariant is a vector space over Z/2 and has a conjectured relationship to Tait colorings of K when K is planar. In this talk, we will explore a variant of this construction, replacing SO(3) with SU(3). With this modified version, the dimension of the instanton homology is indeed equal to the number of Tait colorings when K is planar. (Without the assumption of planarity, the dimension is sometimes larger, sometimes smaller.) There is a further variant, with rational coefficients, whose dimension is equal to the number of Tait colorings always.

Coauthors: Tom Mrowka (MIT)

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University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons