Algebraic & Geometric Topology Volume 16, issue 2 (2016)

Download this article
	For screen
	For printing

Recent Issues

The Journal

About the Journal

Editorial Board

Editorial Interests

Submission Guidelines

Submission Page

Policies for Authors

Ethics Statement

ISSN (electronic): 1472-2739

ISSN (print): 1472-2747

Other MSP Journals

Morse theory for manifolds with boundary

Maciej Borodzik, András Némethi and Andrew Ranicki

Algebraic & Geometric Topology 16 (2016) 971–1023

DOI: 10.2140/agt.2016.16.971

Bibliography

1	V I Arnol′d, S M Guseĭn-Zade, A N Varchenko, Singularities of differentiable maps, I : The classification of critical points, caustics and wave fronts, 82, Birkhäuser (1985) MR777682
2	J M Bloom, The combinatorics of Morse theory with boundary, from: "Proceedings of the Gökova Geometry–Topology Conference 2012" (editors S Akbulut, D Auroux, T Önder), Int. Press (2013) 43 MR3203357
3	M Borodzik, A Némethi, A Ranicki, Codimension 2 embeddings, algebraic surgery and Seifert forms, preprint (2012) arXiv:1211.5964
4	M Borodzik, A Némethi, A Ranicki, On the semicontinuity of the mod 2 spectrum of hypersurface singularities, J. Algebraic Geom. 24 (2015) 379 MR3311588
5	D Braess, Morse-Theorie für berandete Mannigfaltigkeiten, Math. Ann. 208 (1974) 133 MR0348790
6	M Goresky, R MacPherson, Stratified Morse theory, 14, Springer (1988)
7	B Hajduk, Minimal m–functions, Fund. Math. 111 (1981) 179 MR611759
8	A Jankowski, R Rubinsztein, Functions with non-degenerate critical points on manifolds with boundary, Comment. Math. Prace Mat. 16 (1972) 99 MR0331409
9	P Kronheimer, T Mrowka, Monopoles and three-manifolds, 10, Cambridge Univ. Press (2007) MR2388043
10	F Laudenbach, A Morse complex on manifolds with boundary, Geom. Dedicata 153 (2011) 47 MR2819662
11	J Milnor, Morse theory, 51, Princeton Univ. Press (1963) MR0163331
12	J Milnor, Lectures on the h–cobordism theorem, Princeton Univ. Press (1965) MR0190942
13	L I Nicolaescu, An invitation to Morse theory, Springer (2007) MR2298610
14	A Ranicki, High-dimensional knot theory : Algebraic surgery in codimension 2, Springer (1998) MR1713074
15	D Salamon, Morse theory, the Conley index and Floer homology, Bull. London Math. Soc. 22 (1990) 113 MR1045282
16	S Smale, On gradient dynamical systems, Ann. Math. 74 (1961) 199 MR0133139
17	S Smale, On the structure of manifolds, Amer. J. Math. 84 (1962) 387 MR0153022
18	E Witten, Supersymmetry and Morse theory, J. Differential Geom. 17 (1982) 661 MR683171