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Extending families of homeomorphisms over 4-dimensional handlebodies

Geometric Topology 2026-05-27 v1 Algebraic Topology

Abstract

Let HgH_g denote the 4-dimensional handlebody of genus gg and UgU_g its boundary. We show that for all g0g \ge 0 the map from BHomeo(Hg)B Homeo(H_g) to BHomeo(Ug)B Homeo(U_g) induced by restriction to the boundary admits a section.

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Cite

@article{arxiv.2503.19989,
  title  = {Extending families of homeomorphisms over 4-dimensional handlebodies},
  author = {Rachael Boyd and Corey Bregman and Jan Steinebrunner},
  journal= {arXiv preprint arXiv:2503.19989},
  year   = {2026}
}

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11 pages