Algebraic & Geometric Topology Volume 13, issue 1 (2013)

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Cascades and perturbed Morse–Bott functions

Augustin Banyaga and David E Hurtubise

Algebraic & Geometric Topology 13 (2013) 237–275

DOI: 10.2140/agt.2013.13.237

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 ℒG_N,N+K(ℂ), 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