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1999 | 47 | 1 | 233-246
Tytuł artykułu

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

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
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.
Słowa kluczowe
Rocznik
Tom
47
Numer
1
Strony
233-246
Opis fizyczny
Daty
wydano
1999
Twórcy
  • Dipartimento di Scienze Matematiche, Università degli Studi di Trieste, Piazzale Europa, 1, 34100 Trieste, Italy
  • Fachbereich Mathematik, Universität Rostock, Universitätsplatz 1, 18055 Rostock, Germany
Bibliografia
  • [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.
  • [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.
  • [6] A. Floer, Morse theory for Lagrangian intersections, J. Diff. Geometry 28, 1988, 513-547.
  • [7] A. Floer, An instanton-invariant for 3-manifolds, Commun. Math. Physics 118, 1988, 215-240.
  • [8] A. Floer, Symplectic fixed points and holomorphic spheres, Commun. Math. Physics 120, 1989, 575-611.
  • [9] M. Rinaldi and K. P. Rybakowski, Tubular neighborhoods and the gluing principle in Floer homology theory, to appear.
  • [10] K. P. Rybakowski, On the homotopy index for infinite-dimensional semiflows, Trans. Amer. Math. Soc. 269, 1982, 351-382.
  • [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.
  • [12] K. P. Rybakowski, The Homotopy Index and Partial Differential Equations, Springer Verlag, Berlin, Heidelberg, New York, 1987.
  • [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.
  • [14] M. Schwarz, Morse Homology, Birkhäuser Verlag, Basel, Boston, Berlin, 1993.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-bcpv47i1p233bwm
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