Work

Knot lattice homology and $q$-series invariants for plumbed knot complements

Year: 2025

Type: article

Abstract: We introduce an invariant of negative definite plumbed knot complements unifying knot lattice homology, due to Ozsváth, Stipsicz, and Szabó, and the BPS q -series of Gukov and Manolescu. This invariant is a natural extension of weighted graded roots of negative definite plumbed 3-manifolds introduced earlier by the first two authors and Krushkal. We prove a surgery formula relating our invariant to the weighted graded root of the surgered 3-manifold.

Source: Quantum Topology

DOI: 10.4171/qt/236

Authors: Rostislav Akhmechet, Peter K. Johnson, Sunghyuk Park

Institutions: Columbia University, Harvard University

Language: English

Topic: Geometric and Algebraic Topology

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: diamond

Funder: National Science Foundation

Award: RTG: Geometry and Topology at the University of Virginia