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We use Heegaard Floer homology to define an invariant of homology cobordism. This invariant is isomorphic to a summand of the reduced Heegaard Floer homology of a rational homology sphere equipped with a spin structure and is analogous to Stoffregen’s connected Seiberg–Witten Floer homology. We use this invariant to study the structure of the homology cobordism group and, along the way, compute the involutive correction terms $$\bar{d}$$ and $$\text{}\underline{d}$$ for certain families of three-manifolds.
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This content will become publicly available on December 1, 2025
Curvature operators and rational cobordism
We determine linear inequalities on the eigenvalues of curvature operators that imply vanishing of the twisted A-hat genus on a closed Riemannian spin manifold, where the twisting bundle is any prescribed parallel bundle of tensors. These inequalities yield surgery-stable curvature conditions tailored to annihilate further rational cobordism invariants, such as the Witten genus, elliptic genus, signature, and even the rational cobordism class itself.
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- PAR ID:
- 10561782
- Publisher / Repository:
- Elsevier
- Date Published:
- Journal Name:
- Advances in Mathematics
- Volume:
- 458
- Issue:
- PB
- ISSN:
- 0001-8708
- Page Range / eLocation ID:
- 109995
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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