Topological mapping class groups of non-simply connected 4-manifolds

@misc{cha2026topological,
  title = {{Topological mapping class groups of non-simply connected 4-manifolds}},
  author = {Jae Choon Cha},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.26400},
  eprint = {2610.26400},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.26400},
}

TY  - UNPB
TI  - Topological mapping class groups of non-simply connected 4-manifolds
AU  - Jae Choon Cha
PY  - 2026
DA  - 2026/10/19
PB  - arXiv
DO  - 10.48550/arxiv.2610.26400
UR  - https://arxiv.org/abs/2610.26400
AB  - We construct topological isotopy invariants of homeomorphisms of non-simply connected 4-manifolds using the topological Dax invariant of disks and the Freedman-Quinn invariant of spheres. Our invariants are effective for various non-smoothable 4-manifolds without assuming that the fundamental groups are good. They detect infinite-rank free abelian direct factors of the pseudoisotopy-trivial and homotopy-trivial mapping class groups, and give lower bounds on the Prüfer rank of the Torelli groups modulo homotopy-trivial mapping classes, including examples of infinite Prüfer rank. Our method is also useful for smooth 4-manifolds. We construct stably smoothable homeomorphisms of the Enriques surface and many Dolgachev surfaces that act trivially on homology but are not homotopic to the identity.
ER  -