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Geometry and Topology Seminar

Friday, April 12, 2024
4:00pm to 5:00pm
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Online Event
Surgery Exact Triangles in Instanton Theory
Deeparaj Bhat, Department of Mathematics, MIT,

We prove an exact triangle relating the knot instanton homology to the instanton homology of surgeries along the knot. As the knot instanton homology is computable in many instances, this sheds some light on the instanton homology of closed 3-manifolds. We illustrate this with computations in the case of some surgeries on the trefoil. In particular, we show the Poincaré homology sphere is not an instanton L-space (with Z/2 coefficients), in contrast with Heegaard Floer and monopole Floer theories. Finally, we sketch the proof of the triangle inspired by the Atiyah-Floer conjecture and results from symplectic geometry.

For more information, please contact Math Department by phone at 626-395-4335 or by email at [email protected] or visit