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Presented By: Department of Mathematics

Geometry & Physics Seminar

Birational Calabi-Yau Manifolds have Isomorphic Hamiltonian Floer Cohomology Algebras

We show that any two birational projective Calabi-Yau manifolds admit Hamiltonians with isomorphic Hamiltonian Floer cohomology algebras, after a certain change of Novikov rings. As a result, we show that such Calabi-Yau manifolds have isomorphic integral cohomology groups and also isomorphic small quantum cohomology rings after a change of Novikov rings. The proof is inspired by ongoing work of Borman and Sheridan and uses ideas from work by Groman, Venkatesh and Varulgunes. We construct Hamiltonians whose flow `wraps' around certain singular subvarieties of our Calabi-Yau manifolds and use them to construct a symplectic cohomology group. One then shows these respective symplectic cohomology groups are isomorphic. Speaker(s): Mark McLean (Stony Brook)

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