Vanishing homology |
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Authors: | Guillaume Valette |
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Institution: | 1. Department of Mathematics, University of Toronto, 40 St. George st, Toronto, ON, M5S 2E4, Canada 2. Instytut Matematyczny PAN, ul. ?w. Tomasza 30, 31-027, Kraków, Poland
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Abstract: | In this paper, we introduce a new homology theory devoted to the study of families such as semialgebraic or subanalytic families,
and in general, to any family definable in an o-minimal structure (such as Denjoy–Carleman definable, or ln-exp definable
sets). The idea is to study the cycles that are vanishing when we approach a special fiber. This also enables us to derive
local metric invariants for germs of definable sets. We prove that the homology groups are finitely generated. |
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Keywords: | |
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