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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.

Some topics concerning homeomorphic parameterizations.

Stephen Semmes (2001)

Publicacions Matemàtiques

In this survey, we consider several questions pertaining to homeomorphisms, including criteria for their existence in certain circumstances, and obstructions to their existence.

Spaces of polynomials with roots of bounded multiplicity

M. Guest, A. Kozlowski, K. Yamaguchi (1999)

Fundamenta Mathematicae

We describe an alternative approach to some results of Vassiliev ([Va1]) on spaces of polynomials, by applying the "scanning method" used by Segal ([Se2]) in his investigation of spaces of rational functions. We explain how these two approaches are related by the Smale-Hirsch Principle or the h-Principle of Gromov. We obtain several generalizations, which may be of interest in their own right.

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