Algebraic & Geometric Topology

Morse theory for manifolds with boundary

Maciej Borodzik, András Némethi, and Andrew Ranicki

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Abstract

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.

Article information

Source
Algebr. Geom. Topol., Volume 16, Number 2 (2016), 971-1023.

Dates
Received: 23 March 2015
Accepted: 14 August 2015
First available in Project Euclid: 16 November 2017

Permanent link to this document
https://projecteuclid.org/euclid.agt/1510841158

Digital Object Identifier
doi:10.2140/agt.2016.16.971

Mathematical Reviews number (MathSciNet)
MR3493413

Zentralblatt MATH identifier
1342.57018

Subjects
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

Keywords
Morse theory manifold with boundary cobordism bifurcation of singular points

Citation

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


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