Algebraic & Geometric Topology

Morse theory for manifolds with boundary

Maciej Borodzik, András Némethi, and Andrew Ranicki

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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

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

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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

Morse theory manifold with boundary cobordism bifurcation of singular points


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.

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