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A homological approach to Dax invariants
Abstract
We present a homological construction of Dax invariants in 4-manifolds that is intrinsic to the topological category and requires neither smoothing nor generic representatives. Applications include an extension of the invariant of Cha-Kim to neat disks without assuming local flatness, and a topological definition of the Dax map for arc spaces that yields a short alternative proof of the topological Dax isomorphism theorem.
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BibTeX
@misc{cha2026homological,
title = {{A homological approach to Dax invariants}},
author = {Jae Choon Cha},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.30837},
eprint = {2610.30837},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.30837},
}
RIS
TY - UNPB
TI - A homological approach to Dax invariants
AU - Jae Choon Cha
PY - 2026
DA - 2026/10/22
PB - arXiv
DO - 10.48550/arxiv.2610.30837
UR - https://arxiv.org/abs/2610.30837
AB - We present a homological construction of Dax invariants in 4-manifolds that is intrinsic to the topological category and requires neither smoothing nor generic representatives. Applications include an extension of the invariant of Cha-Kim to neat disks without assuming local flatness, and a topological definition of the Dax map for arc spaces that yields a short alternative proof of the topological Dax isomorphism theorem.
ER -