Volume 13, issue 1 (2013)

Download this article
Download this article For screen
For printing
Recent Issues

Volume 22
Issue 6, 2533–3057
Issue 5, 2007–2532
Issue 4, 1497–2006
Issue 3, 991–1495
Issue 2, 473–990
Issue 1, 1–472

Volume 21, 7 issues

Volume 20, 7 issues

Volume 19, 7 issues

Volume 18, 7 issues

Volume 17, 6 issues

Volume 16, 6 issues

Volume 15, 6 issues

Volume 14, 6 issues

Volume 13, 6 issues

Volume 12, 4 issues

Volume 11, 5 issues

Volume 10, 4 issues

Volume 9, 4 issues

Volume 8, 4 issues

Volume 7, 4 issues

Volume 6, 5 issues

Volume 5, 4 issues

Volume 4, 2 issues

Volume 3, 2 issues

Volume 2, 2 issues

Volume 1, 2 issues

The Journal
About the Journal
Editorial Board
Editorial Interests
Subscriptions
 
Submission Guidelines
Submission Page
Policies for Authors
Ethics Statement
 
ISSN (electronic): 1472-2739
ISSN (print): 1472-2747
Author Index
To Appear
 
Other MSP Journals
Cascades and perturbed Morse–Bott functions

Augustin Banyaga and David E Hurtubise

Algebraic & Geometric Topology 13 (2013) 237–275
Bibliography
1 A Abbondandolo, P Majer, Lectures on the Morse complex for infinite-dimensional manifolds, from: "Morse theoretic methods in nonlinear analysis and in symplectic topology" (editors P Biran, O Cornea, F Lalonde), NATO Sci. Ser. II Math. Phys. Chem. 217, Springer (2006) 1 MR2276948
2 R Abraham, J Robbin, Transversal mappings and flows, W. A. Benjamin (1967) MR0240836
3 D M Austin, P J Braam, Morse–Bott theory and equivariant cohomology, from: "The Floer memorial volume" (editors H Hofer, C H Taubes, A Weinstein, E Zehnder), Progr. Math. 133, Birkhäuser (1995) 123 MR1362827
4 A Banyaga, D Hurtubise, Lectures on Morse homology, 29, Kluwer (2004) MR2145196
5 A Banyaga, D E Hurtubise, A proof of the Morse–Bott lemma, Expo. Math. 22 (2004) 365 MR2075744
6 A Banyaga, D E Hurtubise, The Morse–Bott inequalities via a dynamical systems approach, Ergodic Theory Dynam. Systems 29 (2009) 1693 MR2563088
7 A Banyaga, D E Hurtubise, Morse–Bott homology, Trans. Amer. Math. Soc. 362 (2010) 3997 MR2608393
8 R Bott, Morse theory indomitable, Inst. Hautes Études Sci. Publ. Math. 68 (1988) 99 MR1001450
9 F Bourgeois, A Morse–Bott approach to contact homology, from: "Symplectic and contact topology: interactions and perspectives" (editors Y Eliashberg, B Khesin, F Lalonde), Fields Inst. Commun. 35, Amer. Math. Soc. (2003) 55 MR1969267
10 F Bourgeois, A Oancea, An exact sequence for contact- and symplectic homology, Invent. Math. 175 (2009) 611 MR2471597
11 F Bourgeois, A Oancea, Symplectic homology, autonomous Hamiltonians, and Morse–Bott moduli spaces, Duke Math. J. 146 (2009) 71 MR2475400
12 C H Cho, H Hong, Orbifold Morse–Smale–Witten complex arXiv:1103.5528v2
13 K Cieliebak, U A Frauenfelder, A Floer homology for exact contact embeddings, Pacific J. Math. 239 (2009) 251 MR2461235
14 O Cornea, A Ranicki, Rigidity and gluing for Morse and Novikov complexes, J. Eur. Math. Soc. 5 (2003) 343 MR2017851
15 M Farber, Topology of closed one-forms, 108, American Mathematical Society (2004) MR2034601
16 U Frauenfelder, The Arnold–Givental conjecture and moment Floer homology, Int. Math. Res. Not. 2004 (2004) 2179 MR2076142
17 M W Hirsch, Differential topology, 33, Springer (1976) MR0448362
18 D E Hurtubise, The flow category of the action functional on GN,N+K(), Illinois J. Math. 44 (2000) 33 MR1731380
19 D E Hurtubise, Multicomplexes and spectral sequences, J. Algebra Appl. 9 (2010) 519 MR2718643
20 C K R T Jones, Geometric singular perturbation theory, from: "Dynamical systems" (editor R Johnson), Lecture Notes in Math. 1609, Springer (1995) 44 MR1374108
21 C K R T Jones, S K Tin, Generalized exchange lemmas and orbits heteroclinic to invariant manifolds, Discrete Contin. Dyn. Syst. Ser. S 2 (2009) 967 MR2552128
22 J Latschev, Gradient flows of Morse–Bott functions, Math. Ann. 318 (2000) 731 MR1802508
23 J J Leth, Morse–Smale functions and the space of height-parametrized flow lines, PhD thesis, Aalborg University (2007)
24 J R Munkres, Topology: A first course, Prentice-Hall (1975) MR0464128
25 L I Nicolaescu, An invitation to Morse theory, Springer (2007) MR2298610
26 J Palis, On Morse–Smale dynamical systems, Topology 8 (1969) 385 MR0246316
27 S Schecter, Exchange lemmas, I : Deng’s lemma, J. Differential Equations 245 (2008) 392 MR2428004
28 S Schecter, Exchange lemmas, II : General exchange lemma, J. Differential Equations 245 (2008) 411 MR2428005
29 M Schwarz, Morse homology, 111, Birkhäuser (1993) MR1239174
30 J Swoboda, Morse homology for the Yang–Mills gradient flow, J. Math. Pures Appl. 98 (2012) 160 MR2944375