Moderately Discontinuous Homology
نویسندگان
چکیده
Abstract We introduce a new metric homology theory, which we call Moderately Discontinuous Homology, designed to capture Lipschitz properties of singular subanalytic germs. The main novelty our approach is allow “moderately discontinuous” chains, are specially advantageous for capturing the subtleties outer phenomena. Our invariant finitely generated graded abelian group any and homomorphisms . Here “discontinuity rate”. groups germ with inner or proved be only many essential. For Homology recovers tangent cone Gromov one. In general, ‐Homology punctured germ. Hence, can seen as an algebraic interpolating from its cone. theory bi‐Lipschitz invariant, by suitable homotopies, satisfies versions relative Mayer‐Vietoris long exact sequences. Moreover, fixed discontinuity rate b show that it functorial class discontinuous maps, whose discontinuities ‐moderated; this makes quite flexible. complex analytic setting enhancement called Framed MD homology, takes into account information fundamental classes. As applications prove characterizes smooth germs among all germs, number irreducible components embedded topological type plane branches. curve singularity multiplicities © 2020 Wiley Periodicals LLC.
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ژورنال
عنوان ژورنال: Communications on Pure and Applied Mathematics
سال: 2021
ISSN: ['1097-0312', '0010-3640']
DOI: https://doi.org/10.1002/cpa.22013