Homeomorphisms of Bagpipes

zbMath1271.57067arXiv0910.0924MaRDI QIDQ4907412

David B. Gauld

Publication date: 1 February 2013

Abstract: We investigate the mapping class group of an orientable $omega$-bounded surface. Such a surface splits, by Nyikos's Bagpipe Theorem, into a union of a bag (a compact surface with boundary) and finitely many long pipes. The subgroup consisting of classes of homeomorphisms fixing the boundary of the bag is a normal subgroup and is a homomorphic image of the product of mapping class groups of the bag and the pipes.

Full work available at URL: https://arxiv.org/abs/0910.0924

zbMATH Keywords

mapping class grouplong pipegroup of homeomorphisms\(\omega \)-bounded surfacebagpipe surface

Mathematics Subject Classification ID

Transformation groups and semigroups (topological aspects) (54H15) Dynamical systems involving homeomorphisms and diffeomorphisms of planes and surfaces (37E30) Topological properties of groups of homeomorphisms or diffeomorphisms (57S05)

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