An extension of Taubes' Gromov invariant to Calabi--Yau 3-folds

An extension of Taubes' Gromov invariant to Calabi--Yau 3-folds

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Mohan Swaminathan, Princeton University
Fine Hall 314

In-Person and Online Talk

Zoom link: https://princeton.zoom.us/j/453512481?pwd=OHZ5TUJvK2trVVlUVmJLZkhIRHFDUT09

I will describe the construction of a virtual count of embedded pseudo-holomorphic curves of a given genus in a Calabi--Yau 3-fold lying in two times a primitive homology class. The result is an integer-valued symplectic deformation invariant which can be viewed as an analogue of Taubes' Gromov invariant (which is defined for symplectic 4-manifolds). The construction depends on a detailed bifurcation analysis of the moduli space of embedded curves along a generic path of almost complex structures and is partly motivated by Wendl's recent resolution of Bryan--Pandharipande's super-rigidity conjecture.

This is based on joint work with Shaoyun Bai.