Exotic Dehn twists on sums of 4-manifolds, nuclei, and exotic structures

@misc{konno2026exotic,
  title = {{Exotic Dehn twists on sums of 4-manifolds, nuclei, and exotic structures}},
  author = {Hokuto Konno},
  howpublished = {arXiv},
  year = {2026},
  month = nov,
  doi = {10.48550/arxiv.2611.04541},
  eprint = {2611.04541},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2611.04541},
}

TY  - UNPB
TI  - Exotic Dehn twists on sums of 4-manifolds, nuclei, and exotic structures
AU  - Hokuto Konno
PY  - 2026
DA  - 2026/11/03
PB  - arXiv
DO  - 10.48550/arxiv.2611.04541
UR  - https://arxiv.org/abs/2611.04541
AB  - For closed 4-manifolds X_1, X_2, we give a sufficient condition, in terms of the Seiberg-Witten invariants of X_i, for the Dehn twist on X_1#X_2 along the neck to be smoothly nontrivial. This provides a broad generalization of the result of Kronheimer-Mrowka for K3#K3. We also show that the boundary Dehn twists on the punctured connected sums of many pairs of elliptic surfaces are smoothly nontrivial. We also detect new examples of exotic Dehn twists along Seifert fibered 3-manifolds in elliptic surfaces. As a consequence, we exhibit a new phenomenon in which "exotic diffeomorphisms detect exotic smooth structures on 4-manifolds": the triviality of the boundary Dehn twist characterizes the standard nucleus N(n) among the nuclei N(n)_p,q homeomorphic to it, provided that n≡0 bmod 4. These results are proved by computing the families Bauer-Furuta invariant for a new framing of the families Dirac index.
ER  -