Cobordisms of fold maps and maps with prescribed number of cusps
| dc.creator | Ekholm, Tobias | |
| dc.creator | Szucs, Andras | |
| dc.creator | Terpai, Tamas | |
| dc.date | 2007-01-16 | |
| dc.date.accessioned | 2026-07-07T07:41:17Z | |
| dc.date.available | 2026-07-07T07:41:17Z | |
| dc.description | A 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.description | 14 pages, 1 figure | |
| dc.identifier | https://arxiv.org/abs/math/0701433 | |
| dc.identifier | http://arxiv.org/abs/math/0701433 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/122050 | |
| dc.subject | Geometric Topology | |
| dc.subject | 57R45; 57R90 | |
| dc.title | Cobordisms of fold maps and maps with prescribed number of cusps | |
| dc.type | text |