Embedded spheres in S^2\times S^1#...#S^2\times S^1

dc.creatorGadgil, Siddhartha
dc.date2004-10-04
dc.date.accessioned2026-07-07T05:12:49Z
dc.date.available2026-07-07T05:12:49Z
dc.descriptionWe give an algorithm to decide which elements of pi_2(S^2\times S^1#...#S^2\times S^1) can be represented by embedded spheres. Such spheres correspond to splittings of the free group on k generators. Equivalently our algorithm decides whether, for a handlebody N, an element in pi_2(N,\partial N) can be represented by an embedded disc. We also give an algorithm to decide when classes in $π_2(S^2\times S^1#...#S^2\times S^1)$ can be represented by disjoint embedded spheres. We introduce the splitting complex of a free group which is analogous to the complex of curves of a surface. We show that the splitting complex of the free group on k generators embeds in the complex of curves of a surface of genus $k$ as a quasi-convex subset.
dc.description8 pages
dc.identifierhttps://arxiv.org/abs/math/0410047
dc.identifierhttp://arxiv.org/abs/math/0410047
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/72723
dc.subjectGeometric Topology
dc.subjectGroup Theory
dc.subject57M05 ; 57M07, 20E06
dc.titleEmbedded spheres in S^2\times S^1#...#S^2\times S^1
dc.typetext

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