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Uniqueness of models in persistent homology: the case of curves
Persistent Betti numbers reflections matching distance
2011/2/28
We consider generic curves in R2, i.e. generic C1 functions f : S1 → R2.We analyze these curves through the persistent homology groups of a filtration induced on S1 by f. In particular, we consider th...
Generic deformations of the colored sl(N)-homology for links
the colored sl(N)-homology for links math
2010/11/15
We generalize the works of Lee [arXiv:math/0210213v3] and Gornik [arXiv:math/0402266v2] to construct a basis for generic deformations of the colored sl(N)-homology defined in [arXiv:1002.2662v1]. As a...
Partial open book decompositions and the contact class in sutured floer homology
Partial open book decomposition contact three-manifold with convex boundary sutured manifold sutured Floer homology EH-contact class
2010/2/25
We demonstrate how to combinatorially calculate the EH-class of a compatible contact structure in the sutured Floer homology group of a balanced sutured three manifold which is associated to an abstra...
Cyclic homology of commutative algebras over general ground rings
Cyclic homology commutative algebras general ground rings
2010/11/1
We consider commutative algebras and chain DG algebras over a fixed commutative ground ring $k$ as in the title. We are concerned with the problem of computing the cyclic (and Hochschild) homology of...