Papers by J. Edson Sampaio
Communications on Pure and Applied Mathematics, 2021
In this paper we introduce a new metric homology theory, which we call Moderately Discontinuous H... more In this paper we introduce a new metric homology theory, which we call Moderately Discontinuous Homology. The basic idea involves the following basic ideas: first we define a singular homology theory whose simplexes are families of singular chains depending on a parameter t in (0,1), so that the distance from the support of the chain to the singularity approaches the singularity at speed 1 with respect to the parameter. Second, we allow b-moderately discontinuous chains for a certain discontinuity rate b in ranging from 1 to infinity. Combining the homology group obtained for the different discontinuity rates, we obtain an algebraic invariant that is given by a graded abelian group for any b and homomorphisms between these groups. We prove finitely generation, for b equal to infinity it recovers the homology of the punctured germ, and for b=1 it recovers the homology of the tangent cone. Our homology theory is a bi-Lipschitz subanalitic invariant, is invariant by suitable metric hom...
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Papers by J. Edson Sampaio