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Title: Spectrally similar incommensurable 3-manifolds: SPECTRALLY SIMILAR INCOMMENSURABLE 3-MANIFOLDS
Author(s) / Creator(s):
Publisher / Repository:
DOI PREFIX: 10.1112
Date Published:
Journal Name:
Proceedings of the London Mathematical Society
Page Range / eLocation ID:
411 to 447
Medium: X
Sponsoring Org:
National Science Foundation
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  1. Abstract

    By studying the properties ofq-series$$\widehat{Z}$$Z^-invariants, we develop a dictionary between 3-manifolds and vertex algebras. In particular, we generalize previously known entries in this dictionary to Lie groups of higher rank, to 3-manifolds with toral boundaries, and to BPS partition functions with line operators. This provides a new physical realization of logarithmic vertex algebras in the framework of the 3d-3d correspondence and opens new avenues for their future study. For example, we illustrate how invoking a knot-quiver correspondence for$$\widehat{Z}$$Z^-invariants leads to many infinite families of new fermionic formulae for VOA characters.

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