H̃-cobordisms, infinite cyclic covers, and real Seiberg--Witten theory
Abstract
We study H̃-cobordisms of distinguished homology handles, introduced by Kawauchi in 1976 using infinite cyclic covers. Despite the extensive development of gauge-theoretic and Floer-theoretic invariants since Kawauchi's work, none were previously known to distinguish smooth and topological H̃-cobordism. In this paper, we construct asymptotic invariants of distinguished homology handles by applying real Seiberg--Witten theory to finite cyclic covers. Using these invariants, we show that the kernel of the natural map from the smooth H̃-cobordism group to its topological counterpart contains a subgroup isomorphic to ℤ. We also define spin versions of these groups and show that the kernel of the corresponding natural map contains a subgroup isomorphic to ℤ∞.
Related
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BibTeX
@misc{kang2026hcobordisms,
title = {{$\widetildeH$-cobordisms, infinite cyclic covers, and real Seiberg--Witten theory}},
author = {Sungkyung Kang and JungHwan Park and Masaki Taniguchi},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.18043},
eprint = {2609.18043},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.18043},
}
RIS
TY - UNPB
TI - H̃-cobordisms, infinite cyclic covers, and real Seiberg--Witten theory
AU - Sungkyung Kang
AU - JungHwan Park
AU - Masaki Taniguchi
PY - 2026
DA - 2026/09/16
PB - arXiv
DO - 10.48550/arxiv.2609.18043
UR - https://arxiv.org/abs/2609.18043
AB - We study H̃-cobordisms of distinguished homology handles, introduced by Kawauchi in 1976 using infinite cyclic covers. Despite the extensive development of gauge-theoretic and Floer-theoretic invariants since Kawauchi's work, none were previously known to distinguish smooth and topological H̃-cobordism. In this paper, we construct asymptotic invariants of distinguished homology handles by applying real Seiberg--Witten theory to finite cyclic covers. Using these invariants, we show that the kernel of the natural map from the smooth H̃-cobordism group to its topological counterpart contains a subgroup isomorphic to ℤ. We also define spin versions of these groups and show that the kernel of the corresponding natural map contains a subgroup isomorphic to ℤ^∞.
ER -