English

On spaces of embeddings of circles in surfaces

Algebraic Topology 2026-01-21 v1 Group Theory Geometric Topology

Abstract

We consider the space of embeddings of finitely many circles that bound disks in non-positively curved surfaces. We index the connected components of this space with finite rooted trees and show that the connected components are classifying spaces of the ``braided" automorphism groups of the associated trees. An intermediate step to proving these results is to construct a strong deformation retract onto the subspace of geometric circles; moreover, this strong deformation retraction is equivariant with respect to transformations of the surface.

Keywords

Cite

@article{arxiv.2601.12450,
  title  = {On spaces of embeddings of circles in surfaces},
  author = {Ryan C. Gelnett},
  journal= {arXiv preprint arXiv:2601.12450},
  year   = {2026}
}

Comments

31 pages, 8 figures