Motivic Donaldson-Thomas invariants and 3-manifolds
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Tue, 02/11/2010 15:45 |
Ben Davison (Oxford) |
Algebraic and Symplectic Geometry Seminar  |
L3 |
| I will describe recent work on motivic DT invariants for 3-manifolds, which are expected to be a refinement of Chern-Simons theory. The conclusion will be that these should be possible to define and work with, but there will be some interesting problems along the way. There will be a discussion of the problem of upgrading the description of the moduli space of flat connections as a critical locus to the problem of describing the fundamental group algebra of a 3-fold as a "noncommutative critical locus," including a recent topological result on obstructions for this problem. I will also address the question of how a motivic DT invariant may be expected to pick up a finer invariant of 3-manifolds than just the fundamental group. | |||