Geometric formulas for Smale invariants of codimension two immersions

Simple item page
dc.creatorEkholm, Tobias
dc.creatorSzucs, Andras
dc.date2000-02-10
dc.date.accessioned2026-07-07T04:33:48Z
dc.date.available2026-07-07T04:33:48Z
dc.descriptionWe give three formulas expressing the Smale invariant of an immersion f of a (4k-1)-sphere into (4k+1)-space. The terms of the formulas are geometric characteristics of any generic smooth map g of any oriented 4k-dimensional manifold, where g restricted to the boundary is an immersion regularly homotopic to f in (6k-1)-space. The formulas imply that if f and g are two non-regularly homotopic immersions of a (4k-1)-sphere into (4k+1)-space then they are also non-regularly homotopic as immersions into (6k-1)-space. Moreover, any generic homotopy in (6k-1)-space connecting f to g must have at least a_k(2k-1)! cusps, where a_k=2 if k is odd and a_k=1 if k is even.
dc.description22 pages, LaTeX2e
dc.identifierhttps://arxiv.org/abs/math/0002076
dc.identifierhttp://arxiv.org/abs/math/0002076
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/58662
dc.subjectGeometric Topology
dc.subject57R42; 57R45
dc.titleGeometric formulas for Smale invariants of codimension two immersions
dc.typetext

Files

Collections

arXiv