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Morse theory for
manifolds with boundary
Maciej Borodzik, András Némethi and Andrew Ranicki |
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Algebraic & Geometric Topology 16 (2016) 971–1023
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Abstract |
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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. |
Keywords
Morse theory, manifold with boundary, cobordism,
bifurcation of singular points
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Mathematical Subject Classification 2010
Primary: 57R19
Secondary: 58E05, 58A05
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References |
Publication
Received: 23 March 2015
Accepted: 14 August 2015
Published: 26 April 2016
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Authors |
| Maciej Borodzik | |
| Institute of Mathematics University of Warsaw ul. Banacha 2 02-097 Warszawa Poland |
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| András Némethi | |
| Alfréd Rényi Institute of
Mathematics Reáltanoda u. 13-15. 1053 Budapest Hungary |
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| Andrew Ranicki | |
| School of Mathematics University of Edinburgh Edinburgh EH9 3JZ UK |
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