Some remarks on tubular neighborhoods and gluing in Morse-Floer homology

Maurizio Rinaldi; Krzysztof Rybakowski

Banach Center Publications (1999)

  • Volume: 47, Issue: 1, page 233-246
  • ISSN: 0137-6934

Abstract

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We discuss the gluing principle in Morse-Floer homology and show that there is a gap in the traditional proof of the converse gluing theorem. We show how this gap can be closed by the use of a uniform tubular neighborhood theorem. The latter result is only stated here. Details are given in the authors' paper, Tubular neighborhoods and the Gluing Principle in Floer homology theory, to appear.

How to cite

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Rinaldi, Maurizio, and Rybakowski, Krzysztof. "Some remarks on tubular neighborhoods and gluing in Morse-Floer homology." Banach Center Publications 47.1 (1999): 233-246. <http://eudml.org/doc/208937>.

@article{Rinaldi1999,
abstract = {We discuss the gluing principle in Morse-Floer homology and show that there is a gap in the traditional proof of the converse gluing theorem. We show how this gap can be closed by the use of a uniform tubular neighborhood theorem. The latter result is only stated here. Details are given in the authors' paper, Tubular neighborhoods and the Gluing Principle in Floer homology theory, to appear.},
author = {Rinaldi, Maurizio, Rybakowski, Krzysztof},
journal = {Banach Center Publications},
keywords = {Floer homology; gluing; tubular neighborhood; converse gluing theorem},
language = {eng},
number = {1},
pages = {233-246},
title = {Some remarks on tubular neighborhoods and gluing in Morse-Floer homology},
url = {http://eudml.org/doc/208937},
volume = {47},
year = {1999},
}

TY - JOUR
AU - Rinaldi, Maurizio
AU - Rybakowski, Krzysztof
TI - Some remarks on tubular neighborhoods and gluing in Morse-Floer homology
JO - Banach Center Publications
PY - 1999
VL - 47
IS - 1
SP - 233
EP - 246
AB - We discuss the gluing principle in Morse-Floer homology and show that there is a gap in the traditional proof of the converse gluing theorem. We show how this gap can be closed by the use of a uniform tubular neighborhood theorem. The latter result is only stated here. Details are given in the authors' paper, Tubular neighborhoods and the Gluing Principle in Floer homology theory, to appear.
LA - eng
KW - Floer homology; gluing; tubular neighborhood; converse gluing theorem
UR - http://eudml.org/doc/208937
ER -

References

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  1. [1] S. Angenent and R. Vandervorst, preprint. 
  2. [2] V. Benci, A new approach to the Morse-Conley theory and some applications, Ann. Mat. Pura Appl. (4) 158, 1991, 231-305. Zbl0778.58011
  3. [3] C. C. Conley, Isolated Invariant Sets and the Morse Index, CBMS 38, AMS, Providence, 1978. 
  4. [4] K. Deimling, Nonlinear Functional Analysis, Springer Verlag, Berlin, Heidelberg, New York, 1985. 
  5. [5] S. K. Donaldson and P. B. Kronheimer, The Geometry of Four-Manifolds, Oxford University Press, 1990. Zbl0820.57002
  6. [6] A. Floer, Morse theory for Lagrangian intersections, J. Diff. Geometry 28, 1988, 513-547. Zbl0674.57027
  7. [7] A. Floer, An instanton-invariant for 3-manifolds, Commun. Math. Physics 118, 1988, 215-240. Zbl0684.53027
  8. [8] A. Floer, Symplectic fixed points and holomorphic spheres, Commun. Math. Physics 120, 1989, 575-611. Zbl0755.58022
  9. [9] M. Rinaldi and K. P. Rybakowski, Tubular neighborhoods and the gluing principle in Floer homology theory, to appear. Zbl0967.53054
  10. [10] K. P. Rybakowski, On the homotopy index for infinite-dimensional semiflows, Trans. Amer. Math. Soc. 269, 1982, 351-382. Zbl0468.58016
  11. [11] K. P. Rybakowski, The Morse index, repeller-attractor pairs and the connection index for semiflows on noncompact spaces, J. Diff. Equations 47, 1983, 66-98. Zbl0468.58015
  12. [12] K. P. Rybakowski, The Homotopy Index and Partial Differential Equations, Springer Verlag, Berlin, Heidelberg, New York, 1987. Zbl0628.58006
  13. [13] K. P. Rybakowski and E. Zehnder, On a Morse equation in Conley's index theory for semiflows in metric spaces, Ergodic Theory Dyn. Systems 5, 1985, 123-143. Zbl0581.54026
  14. [14] M. Schwarz, Morse Homology, Birkhäuser Verlag, Basel, Boston, Berlin, 1993. 

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