Mapping class groups of simply connected closed spin 5-manifolds with no 2- and 3-torsion in homology

@misc{jin2026mapping,
  title = {{Mapping class groups of simply connected closed spin 5-manifolds with no 2- and 3-torsion in homology}},
  author = {Huize Jin},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2608.26698},
  eprint = {2608.26698},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2608.26698},
}

TY  - UNPB
TI  - Mapping class groups of simply connected closed spin 5-manifolds with no 2- and 3-torsion in homology
AU  - Huize Jin
PY  - 2026
DA  - 2026/09/12
PB  - arXiv
DO  - 10.48550/arxiv.2608.26698
UR  - https://arxiv.org/abs/2608.26698
AB  - We show that the Torelli group of a simply connected closed 5-manifold M, which is spin and has no 2-torsion elements in homology, is isomorphic to the bordism group Ω^Spin_6(K(H_2(M), 2)). For H_2(M) with no 2- and 3-torsion we determine this bordism group, and give explicit constructions for the generators of the Torelli group. Furthermore, for the g-fold connected sum #^g(S^2 × S^3) we completely determine its mapping class group. We apply our results to compute the stabilization and abelianization of the mapping class group of #^g(S^2 × S^3), determine the group of isotopy classes of diffeomorphisms of M that are homotopic to the identity, and study the embeddings of S^3 in S^2 × S^3.
ER  -