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Non-kinetic homotopy coherent actions on four-manifolds

  • Sungkyung Kang
  • JungHwan Park
  • Masaki Taniguchi
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Abstract

We give the first example of a non-kinetic smooth homotopy coherent action of order two on a closed simply connected smooth four-manifold. This action is obtained by restricting a nontrivial smooth homotopy coherent action of the discrete circle group on a stabilized K3 surface. We also construct relatively non-kinetic smooth homotopy coherent extensions of boundary involutions over compact smooth $4$-manifolds. In addition, we exhibit boundary involutions that admit locally linear topological extensions but no smooth extensions over the same stabilized fillings. Nevertheless, we prove a Wall-type theorem showing that every free involution on a disjoint union of integral homology spheres extends smoothly over any simply connected smooth filling after sufficiently many stabilizations by S2× S2.

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Cite

BibTeXRIS
BibTeX
@misc{kang2026nonkinetic,
  title = {{Non-kinetic homotopy coherent actions on four-manifolds}},
  author = {Sungkyung Kang and JungHwan Park and Masaki Taniguchi},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2607.24548},
  eprint = {2607.24548},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2607.24548},
}
RIS
TY  - UNPB
TI  - Non-kinetic homotopy coherent actions on four-manifolds
AU  - Sungkyung Kang
AU  - JungHwan Park
AU  - Masaki Taniguchi
PY  - 2026
DA  - 2026/10/21
PB  - arXiv
DO  - 10.48550/arxiv.2607.24548
UR  - https://arxiv.org/abs/2607.24548
AB  - We give the first example of a non-kinetic smooth homotopy coherent action of order two on a closed simply connected smooth four-manifold. This action is obtained by restricting a nontrivial smooth homotopy coherent action of the discrete circle group on a stabilized K3 surface. We also construct relatively non-kinetic smooth homotopy coherent extensions of boundary involutions over compact smooth $4$-manifolds. In addition, we exhibit boundary involutions that admit locally linear topological extensions but no smooth extensions over the same stabilized fillings. Nevertheless, we prove a Wall-type theorem showing that every free involution on a disjoint union of integral homology spheres extends smoothly over any simply connected smooth filling after sufficiently many stabilizations by S^2× S^2.
ER  -