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Article contents
Global index of real polynomials
Part of:
Differential topology
Theory of singularities and catastrophe theory
Curves
Fiber spaces and bundles
Published online by Cambridge University Press: 18 March 2024
Abstract
We develop two methods for expressing the global index of the gradient of a 2 variable polynomial function $f$
: in terms of the atypical fibres of $f$
, and in terms of the clusters of Milnor arcs at infinity. These allow us to derive upper bounds for the global index, in particular refining the one that was found by Durfee in terms of the degree of $f$
.
MSC classification
- Type
- Research Article
- Information
- Copyright
- Copyright © The Author(s), 2024. Published by Cambridge University Press on behalf of The Royal Society of Edinburgh
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