# 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

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topRinaldi, 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

top- [1] S. Angenent and R. Vandervorst, preprint.
- [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] C. C. Conley, Isolated Invariant Sets and the Morse Index, CBMS 38, AMS, Providence, 1978.
- [4] K. Deimling, Nonlinear Functional Analysis, Springer Verlag, Berlin, Heidelberg, New York, 1985.
- [5] S. K. Donaldson and P. B. Kronheimer, The Geometry of Four-Manifolds, Oxford University Press, 1990. Zbl0820.57002
- [6] A. Floer, Morse theory for Lagrangian intersections, J. Diff. Geometry 28, 1988, 513-547. Zbl0674.57027
- [7] A. Floer, An instanton-invariant for 3-manifolds, Commun. Math. Physics 118, 1988, 215-240. Zbl0684.53027
- [8] A. Floer, Symplectic fixed points and holomorphic spheres, Commun. Math. Physics 120, 1989, 575-611. Zbl0755.58022
- [9] M. Rinaldi and K. P. Rybakowski, Tubular neighborhoods and the gluing principle in Floer homology theory, to appear. Zbl0967.53054
- [10] K. P. Rybakowski, On the homotopy index for infinite-dimensional semiflows, Trans. Amer. Math. Soc. 269, 1982, 351-382. Zbl0468.58016
- [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] K. P. Rybakowski, The Homotopy Index and Partial Differential Equations, Springer Verlag, Berlin, Heidelberg, New York, 1987. Zbl0628.58006
- [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] M. Schwarz, Morse Homology, Birkhäuser Verlag, Basel, Boston, Berlin, 1993.

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