Department of Mathematics

Geometry and Topology

  •  Peter Johnson, Michigan State University
  •  Knot lattice homology and the Gukov-Manolescu 2-variable series
  •  10/04/2022
  •  3:00 PM - 4:00 PM
  •  C304 Wells Hall (Virtual Meeting Link)
  •  Peter Kilgore Johnson (john8251@msu.edu)

In previous work of Akhmechet, Krushkal, and the speaker, a unification of lattice cohomology and the $\widehat{Z}$-invariant was established. Both theories are combinatorially defined invariants of plumbed 3-manifolds, but with quite different origins. Lattice cohomology, due to Némethi, is motivated by the study of normal surface singularities and is isomorphic to Heegaard Floer homology for plumbing trees. On the other hand, $\widehat{Z}$, due to Gukov-Pei-Putrov-Vafa, is a power series coming from a physical theory and is conjectured to recover quantum invariants of 3-manifolds at roots of unity. In this talk, I will discuss work in progress relating knot lattice homology and the Gukov-Manolescu 2-variable series, the knot theoretic counterparts to lattice homology and $\widehat{Z}$. This is joint work with Ross Akhmechet and Sunghyuk Park.

 

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