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Some homotopy theoretical questions arising in Nielsen coincidence theory

Ulrich Koschorke (2009)

Banach Center Publications

Basic examples show that coincidence theory is intimately related to central subjects of differential topology and homotopy theory such as Kervaire invariants and divisibility properties of Whitehead products and of Hopf invariants. We recall some recent results and ask a few questions which seem to be important for a more comprehensive understanding.

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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