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2026-01-18 15:16 UTC · math.AT · math.AT, math.GR, math.GT

On spaces of embeddings of circles in surfaces

Ryan C. Gelnett

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.
arXiv abstractPDF

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