Atiyah-Bott formula and homological block of Seifert fibered homology $3$-spheres

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abstract

We show that the homological block of Seifert fibered homology $3$-spheres are computed by the iterated use of Atiyah-Bott fixed point formula.

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Nesting behind $\hat{Z}$-invariants
math.RT 2025-07 conditional novelty 6.0 of 10

The paper hypothesizes an abelian categorification of Z-hat invariants for all negative definite plumbed 3-manifolds, with character formulas that formally reproduce the known invariants as virtual generalized characters.
Hypercubic structures behind $\hat{Z}$-invariants
math.RT 2025-01 conditional novelty 6.0 of 10

A hypercubic DAG recursion reproduces the bosonic formula for Z-hat invariants of Seifert manifolds and motivates a conjectural abelian categorification via recursive shift systems.