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