On the topology of semi-algebraic functions on closed semi-algebraic sets

Details On the topology of semi-algebraic functions on closed semi-algebraic sets On the topology of semi-algebraic functions on closed semi-algebraic sets

2010-12-09

arxiv.org/abs/1012.2093v1

Mathematics

Algebraic Geometry

Scientific paper

We consider a semi-algebraic function defined on a closed semi-algebraic set
X. We give formulas relating the topology of X to the indices of the critical
points of the function and to the topological behavior of the function at
infinity. We give applications when X is R^n and when the function is linear.

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