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

Maurizio Rinaldi, Krzysztof Rybakowski (1999)

Banach Center Publications

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.

Stability is not open

Kai Cieliebak, Urs Frauenfelder, Gabriel P. Paternain (2010)

Annales de l’institut Fourier

We give an example of a symplectic manifold with a stable hypersurface such that nearby hypersurfaces are typically unstable.

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