Department of Mathematics

Geometry and Topology

  •  Ross Akhmechet, University of Virginia
  •  Lattice cohomology and q-series invariants of 3-manifolds
  •  07/29/2022
  •  10:30 AM - 11:30 AM
  •  C304 Wells Hall
  •  Teena Meredith Gerhardt (

I will discuss an invariant of negative definite plumbed 3-manifolds which unifies and extends two theories with quite different origins and structures. The first is lattice cohomology, due to Némethi, which is motivated by normal surface singularities and is isomorphic to Heegaard Floer homology for a large class of plumbings. The second theory is the $\widehat{Z}$ series of Gukov-Pei-Putrov-Vafa, a power series which conjecturally recovers SU(2) quantum invariants at roots of unity and satisfies remarkable modularity properties. I will explain lattice cohomology, $\widehat{Z}$, and our unification of these theories. I will also discuss some key features of our new invariant: it leads to a 2-variable refinement of $\widehat{Z}$, and, unlike both lattice cohomology and $\widehat{Z}$, it is sensitive to $spinc^c$-conjugation. This is joint work with Peter Johnson and Slava Krushkal.



Department of Mathematics
Michigan State University
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