On intersection forms of spin $4$-manifolds with AR homology sphere boundary

@misc{hakamada2026intersection,
  title = {{On intersection forms of spin $4$-manifolds with AR homology sphere boundary}},
  author = {Eiichiro Hakamada},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.35931},
  eprint = {2609.35931},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.35931},
}

TY  - UNPB
TI  - On intersection forms of spin $4$-manifolds with AR homology sphere boundary
AU  - Eiichiro Hakamada
PY  - 2026
DA  - 2026/09/28
PB  - arXiv
DO  - 10.48550/arxiv.2609.35931
UR  - https://arxiv.org/abs/2609.35931
AB  - In this paper, building on the work of Dai--Sasahira--Stoffregen, we derive constraints on the intersection forms of smooth, compact, indefinite, spin $4$-manifolds bounded by AR homology spheres using two methods. First, we use the constraints on the existence of Pin(2)-equivariant maps between representation spheres, established by Hopkins--Lin--Shi--Xu in their proof of the 10/8 + 4-inequality. Second, we compute Lin's κo-invariant for AR homology spheres. Combined with Lin's version of the relative 10/8-inequality, this computation yields constraints different from those based on Hopkins--Lin--Shi--Xu. As applications, we obtain new lower bounds on the minimal genus of surfaces bounded by knots whose double branched covers are AR homology spheres in various $4$-manifolds, and provide an obstruction to smooth $4$-manifold decompositions related to the 11/8-conjecture.
ER  -