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PreprintCC BY 4.0arXiv

Simple Slice Surfaces

  • Mark Pencovitch
Open at sourcePDFDOICite

Abstract

Given a simply-connected $4$-manifold with boundary the $3$-sphere, we give sufficient conditions for a knot in the boundary to bound a simply embedded locally flat surface in the $4$-manifold of fixed nonzero genus, representing a fixed nonzero homology class. In certain indefinite cases, we also give conditions for these slice surfaces to be unique up to equivalence.

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Cite

BibTeXRIS
BibTeX
@misc{pencovitch2026simple,
  title = {{Simple Slice Surfaces}},
  author = {Mark Pencovitch},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.22924},
  eprint = {2609.22924},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.22924},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Simple Slice Surfaces
AU  - Mark Pencovitch
PY  - 2026
DA  - 2026/09/19
PB  - arXiv
DO  - 10.48550/arxiv.2609.22924
UR  - https://arxiv.org/abs/2609.22924
AB  - Given a simply-connected $4$-manifold with boundary the $3$-sphere, we give sufficient conditions for a knot in the boundary to bound a simply embedded locally flat surface in the $4$-manifold of fixed nonzero genus, representing a fixed nonzero homology class. In certain indefinite cases, we also give conditions for these slice surfaces to be unique up to equivalence.
ER  -