Cobordisms of fold maps and maps with prescribed number of cusps

dc.creatorEkholm, Tobias
dc.creatorSzucs, Andras
dc.creatorTerpai, Tamas
dc.date2007-01-16
dc.date.accessioned2026-07-07T07:41:17Z
dc.date.available2026-07-07T07:41:17Z
dc.descriptionA generic smooth map of a closed $2k$-manifold into $(3k-1)$-space has a finite number of cusps ($Σ^{1,1}$-singularities). We determine the possible numbers of cusps of such maps. A fold map is a map with singular set consisting of only fold singularities ($Σ^{1,0}$-singularities). Two fold maps are fold bordant if there are cobordisms between their source- and target manifolds with a fold map extending the two maps between the boundaries, if the two targets agree and the target cobordism can be taken as a product with a unit interval then the maps are fold cobordant. We compute the cobordism groups of fold maps of $(2k-1)$-manifolds into $(3k-2)$-space. Analogous cobordism semi-groups for arbitrary closed $(3k-2)$-dimensional target manifolds are endowed with Abelian group structures and described. Fold bordism groups in the same dimensions are described as well.
dc.description14 pages, 1 figure
dc.identifierhttps://arxiv.org/abs/math/0701433
dc.identifierhttp://arxiv.org/abs/math/0701433
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/122050
dc.subjectGeometric Topology
dc.subject57R45; 57R90
dc.titleCobordisms of fold maps and maps with prescribed number of cusps
dc.typetext

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