Geodesic
Morse theory for manifolds with boundary
Borodzik, Maciej1 ; Némethi, András2 ; Ranicki, Andrew3
1Institute of Mathematics, University of Warsaw, ul. Banacha 2, 02-097 Warszawa, Poland
2Alfréd Rényi Institute of Mathematics, Reáltanoda u. 13-15., 1053 Budapest, Hungary
3School of Mathematics, University of Edinburgh, Edinburgh EH9 3JZ, UK
Algebraic and Geometric Topology, Tome 16 (2016) no. 2, pp. 971-1023
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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.

DOI : 10.2140/agt.2016.16.971
Classification : 57R19, 58E05, 58A05
Keywords: Morse theory, manifold with boundary, cobordism, bifurcation of singular points

Borodzik, Maciej  1   ; Némethi, András  2   ; Ranicki, Andrew  3

1 Institute of Mathematics, University of Warsaw, ul. Banacha 2, 02-097 Warszawa, Poland
2 Alfréd Rényi Institute of Mathematics, Reáltanoda u. 13-15., 1053 Budapest, Hungary
3 School of Mathematics, University of Edinburgh, Edinburgh EH9 3JZ, UK 
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Borodzik, Maciej; Némethi, András; Ranicki, Andrew. Morse theory for manifolds with boundary. Algebraic and Geometric Topology, Tome 16 (2016) no. 2, pp. 971-1023. doi: 10.2140/agt.2016.16.971

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