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Surfaces proper homotopy equivalent to graphs and their Dehn-Nielsen-Baer maps

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arxiv 2410.20877 v2 pith:SFLUHCM5 submitted 2024-10-28 math.GT math.GR

classification math.GTmath.GR
keywords homotopysurfacesequivalentgraphproperclassdehn-nielsen-baergraphs
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Motivated by the recent work of Algom-Kfir and Bestinva introducing the mapping class group of an infinite graph via proper homotopy equivalences, we give a necessary and sufficient condition for a surface to be properly homotopy equivalent to a graph. We consider second-countable orientable surfaces that are possibly infinite-type and have noncompact boundary. For surfaces proper homotopy equivalent to graphs, we explore the basic properties of the induced map between the mapping class groups of the surface and the graph. We view this induced map as the basis of a Dehn-Nielsen-Baer analog in the setting of infinite-type surfaces.

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Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Irreducible proper 2-knots from exotic open 2-handles

    math.GT 2026-07 conditional novelty 8.0 of 10

    The paper constructs infinite families of topologically standard but smoothly exotic proper Möbius strips and annuli in R^4 that cannot be built by end-summing with exotic planes, via a new standardization theorem for...

  2. Asymptotically rigid mapping class groups of infinite graphs

    math.GT 2025-08 conditional novelty 7.0 of 10

    Graph Houghton groups form a genuinely new family of Houghton-type groups with finiteness type F_{r-1} but not FP_r, and with explicit presentations of their pure subgroups.

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