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pro vyhledávání: '"Mosquera Lois, David"'
We lift the Lefschetz number from an algebraic invariant of maps between spaces to an invariant of morphisms of data over the spaces.
Comment: 21 pages. All comments are welcome!
Comment: 21 pages. All comments are welcome!
Externí odkaz:
http://arxiv.org/abs/2410.13653
We introduce two novel complementary notions of the Lefschetz number for a functor from a finite acyclic category to itself and we prove a Lefschetz fixed-object theorem and a Lefschetz fixed-morphism theorem. In order to do so, we use the connection
Externí odkaz:
http://arxiv.org/abs/2404.06573
We develop a theory of integration with respect to the Lefschetz number in the context of o-minimal structures containing the semilinear sets. We prove several results and we apply the theory to the field of object detection using sensors.
Externí odkaz:
http://arxiv.org/abs/2312.02909
We extend discrete Morse-Bott theory to the setting of loop-free (or acyclic) categories. First of all, we state a homological version of Quillen's Theorem A in this context and introduce the notion of cellular categories. Second, we present a notion
Externí odkaz:
http://arxiv.org/abs/2107.06202
Publikováno v:
In Topology and its Applications 1 November 2023 339 Part A
Autor:
Fernández Ternero, Desamparados, Macías Virgós, Enrique, Mosquera Lois, David, Vilches Alarcón, José Antonio
Publikováno v:
Journal of Topology and Analysis. :1-24
We develop Morse–Bott theory on posets, generalizing both discrete Morse–Bott theory for regular complexes and Morse theory on posets. Moreover, we prove a Lusternik–Schnirelmann theorem for general matchings on posets, in particular, for Morse
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::dcfe2b15f3b1decb65499982c8075290
https://doi.org/10.1142/s1793525321500709
https://doi.org/10.1142/s1793525321500709
Akademický článek
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Autor:
Fernández Ternero, Desamparados, Macías Virgos, Enrique, Mosquera Lois, David, Vilches Alarcón, José Antonio
We prove a version of the fundamental theorems of Morse theory in the setting of finite partially ordered sets. By using these results we extend Forman's discrete Morse theory to more general cell complexes and derive the Morse-Pitcher inequalities i
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=od______3272::5836ba965a474f4af0d1905557e72607
Autor:
Mosquera Lois, David
Publikováno v:
Minerva. Repositorio Institucional de la Universidad de Santiago de Compostela
instname
instname
Morse Theory and related invariants are studied in the contexts of finite topological spaces, partially ordered sets, chain complexes, cell complexes and small categories. 2023-02-04
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=dedup_wf_001::c84d26bfdd1c8247121b65a7bf6ac6fe
https://hdl.handle.net/10347/27670
https://hdl.handle.net/10347/27670
Autor:
Mosquera Lois, David
Robot motion planning consists in providing a robot some tasks in order to be completed without human intervention. Instabilities which may appear on the algorithms depend on the homotopy type of the configuration space. The aim of this dissertation
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::4556bc690048de60f217087056201f13