Subtleties of the minmax selector

Details Subtleties of the minmax selector Subtleties of the minmax selector

2011-12-22

arxiv.org/abs/1112.5272v1

Mathematics

Symplectic Geometry

12 pages

Scientific paper

In this note, we show that the minmax and maxmin critical values of a
function quadratic nondegenerate at infinity are equal when defined in homology
or cohomology with coefficients in a field. However, by an example of
F.Laudenbach, this is not always true for coefficients in a ring and, even in
the case of a field, the minmax-maxmin depends on the field.

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