Algebraic & Geometric Topology
- Algebr. Geom. Topol.
- Volume 16, Number 2 (2016), 971-1023.
Morse theory for manifolds with boundary
We develop Morse theory for manifolds with boundary. Beside standard and expected facts like the handle cancellation theorem and the Morse lemma for manifolds with boundary, we prove that under suitable connectedness assumptions a critical point in the interior of a Morse function can be moved to the boundary, where it splits into a pair of boundary critical points. As an application, we prove that every cobordism of connected manifolds with boundary splits as a union of left product cobordisms and right product cobordisms.
Algebr. Geom. Topol., Volume 16, Number 2 (2016), 971-1023.
Received: 23 March 2015
Accepted: 14 August 2015
First available in Project Euclid: 16 November 2017
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 57R19: Algebraic topology on manifolds
Secondary: 58E05: Abstract critical point theory (Morse theory, Ljusternik-Schnirelman (Lyusternik-Shnirel m an) theory, etc.) 58A05: Differentiable manifolds, foundations
Borodzik, Maciej; Némethi, András; Ranicki, Andrew. Morse theory for manifolds with boundary. Algebr. Geom. Topol. 16 (2016), no. 2, 971--1023. doi:10.2140/agt.2016.16.971. https://projecteuclid.org/euclid.agt/1510841158