Hostname: page-component-cd9895bd7-8ctnn Total loading time: 0 Render date: 2024-12-27T10:03:44.783Z Has data issue: false hasContentIssue false
  • English
  • Français

Cone-decompositions and degenerate criticalpoints

Published online by Cambridge University Press:  01 September 1998

O Cornea
Get access

Abstract

Let $M$ be a compact, smooth, $2$-connected, $2m$-dimensional manifold with $\partial M$ simply connected. If $M$ has the homotopytype of an $m$-dimensional $CW$-complex, then it supports a smooth, self-indexed function, maximal, constant and regular on $\partial M$ with at most $\mbox{cat}(M)+2$ critical points, all of which are of a certain ‘reasonable’ type. To such a critical point there corresponds, homotopically, the attachment of a cone. Conversely, to a cone attachment we may associate, under certain dimensionality and connectivity conditions, a ‘reasonable’ critical point.

1991 Mathematics Subject Classification: primary 55M30, 57R70; secondary 58E05, 55P50, 55P62.

Keywords

Lusternik-Schnirelmann categorycritical points
Type
Research Article
Information
Proceedings of the London Mathematical Society , Volume 77 , Issue 2 , September 1998 , pp. 437 - 461
Copyright
London Mathematical Society 1998

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)