Witt invariants from q-series $\hat{Z}$
John Chae
TL;DR
This paper establishes a novel connection between Witt invariants of 3-manifolds and $oldsymbol{ ext{ } ext{ extasciitilde} ext{Z}}$-invariants, offering an alternative computational approach and analyzing various homology spheres.
Contribution
It introduces a new method linking Witt invariants to $oldsymbol{ ext{ } ext{ extasciitilde} ext{Z}}$-invariants, simplifying calculations and enabling analysis of complex 3-manifolds.
Findings
Derived a relation between Witt invariants and $oldsymbol{ ext{ } ext{ extasciitilde} ext{Z}}$-invariants.
Applied the method to various homology spheres, including hyperbolic manifolds.
Provided an alternative computational approach for Witt invariants.
Abstract
We present a relation between the Witt invariants of 3-manifolds and the -invariants. It provides an alternative approach to compute the Witt invariants of 3-manifolds, which were originally defined geometrically in four dimensions. We analyze various homology spheres including a hyperbolic manifold using this method.
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Taxonomy
TopicsHomotopy and Cohomology in Algebraic Topology · Geometric and Algebraic Topology · Advanced Combinatorial Mathematics