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o-MINIMAL COHOMOLOGY: FINITENESS AND INVARIANCE RESULTS

ALESSANDRO BERARDUCCI

Università di Pisa, Dipartimento di Matematica, Largo Bruno Pontecorvo 5, 56127 Pisa, Italy

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and

ANTONGIULIO FORNASIERO

Westfälische Wilhelms-Universität Münster, Institut für Mathematische Logik, Einsteinstr. 62, 48149 Münster, Germany

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https://doi.org/10.1142/S0219061309000859Cited by:5 (Source: Crossref)

Abstract

The topology of definable sets in an o-minimal expansion of a group is not fully understood due to the lack of a triangulation theorem. Despite the general validity of the cell decomposition theorem, we do not know whether any definably compact set is a definable CW-complex. Moreover the closure of an o-minimal cell can have arbitrarily high Betti numbers. Nevertheless we prove that the cohomology groups of a definably compact set over an o-minimal expansion of a group are finitely generated and invariant under elementary extensions and expansions of the language.

Keywords:

AMSC: Primary 03C64, Secondary 55N30

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