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Cobordisms of fold maps and maps with a prescribed number of cusps
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics. (Matematik 1-5)
2007 (English)In: Kyushu Journal of Mathematics, ISSN 1340-6116(Print);1883-2032(Online), Vol. 61, no 2, 395-414 p.Article in journal (Refereed) Published
Abstract [en]

A generic smooth map of a closed $2k$-manifold into $(3k-1)$-space has a finite number of cusps ($\Sigma^{1,1}$-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 ($\Sigma^{1,0}$-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.

Place, publisher, year, edition, pages
2007. Vol. 61, no 2, 395-414 p.
Keyword [en]
cobordism, cusp, fold, singularity
National Category
Mathematics
Identifiers
URN: urn:nbn:se:uu:diva-12639DOI: 10.2206/kyushujm.61.395ISI: 000250912800004OAI: oai:DiVA.org:uu-12639DiVA: diva2:40408
Available from: 2008-01-08 Created: 2008-01-08 Last updated: 2011-01-18Bibliographically approved

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Ekholm, Tobias

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