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math.AT2024
An axiomatic treatment of Persistent Homology
Sergio Tsuyoshi Ura, Marco Contessoto, Alice Kimie Miwa Libardi
We develop an axiomatic framework for persistent homology in any degree. We prove the existence and uniqueness for both a persistent version of the Eilenberg-Steenrod axioms for cl…
math.AT2018
Some results on extension of maps and applications
C. Biasi, A. Libardi, T. Melo +1
This paper concerns extension of maps using obstruction theory under a non classical viewpoint. It is given a classification of homotopy classes of maps and as an application it is…
math.AT2014
Cobordism of maps on -Witt spaces
Jean-Paul Brasselet, Alice Kimie Miwa Libardi, Eliris Rizziolli +1
In this article we study the bordism groups of normally nonsingular maps defined on pseudomanifolds and . To characterize the bordism of such maps, inspired by…