Banca de DEFESA: DENILSON TENÓRIO DOS SANTOS JÚNIOR

Uma banca de DEFESA de DOUTORADO foi cadastrada pelo programa.
DISCENTE : DENILSON TENÓRIO DOS SANTOS JÚNIOR
Data: 30/06/2026
HORA: 10:00
LOCAL: Auditório 801 no 8º andar do Bloco B do Campus Santo André da Universidade Federal do ABC
TÍTULO:

Singularity Collisions: Conley Theory and Intersection Homology

PÁGINAS: 259
RESUMO:

This doctoral thesis innovatively presents the definition of collisions of singularities, which can be used to simplify definitions and results previously established for homotopical dynamical cancellations (cancellations) on Gutierrez-Sotomayor (GS) manifolds equipped with a GS flow. This definition allows us to present proofs of results that significantly generalize cancellation results on GS manifolds. Furthermore, we present an in-depth study of two important classes of singular manifolds, obtained through specific process of collisions: generalized GS (GGS) manifolds equipped with a continuous flow and n-pseudomanifolds with isolated singularities whose links are homeomorphic to finite disjoint unions of (n-1)-spheres, which we call pseudomanifolds with cone-type singularities, equipped with singular Morse-Smale flows. For these two classes, we obtain a series of results encompassing the study of Conley theory. Specifically, we present a series of formulas that use dynamical information to obtain the Conley index of the associated isolated invariant sets, we exhibit the construction of global Lyapunov functions, we present a series of formulas and relationships between the Euler-Poincaré characteristic of these singular manifolds and the dynamical and topological aspects of the singularities, and finally, we obtain bounds for the degree of the vertices of the Lyapunov graphs associated with these two classes. Additionally, for the class of GGS manifolds, we present a series of results on homotopical dynamical cancellations. Finally, for the GGS class restricted to cone-type singularities and for the class of pseudomanifolds with cone-type singularities equipped with a singular Morse-Smale flow, we present a study on the intersection homology of these pseudomanifolds and chain complexes that use the respective dynamics to relate intersection homology, Morse homology, and singular homology.

MEMBROS DA BANCA:
Presidente - Interno ao Programa - 1067113 - DAHISY VALADAO DE SOUZA LIMA
Membro Titular - Examinador(a) Externo ao Programa - 1675735 - MARIANA RODRIGUES DA SILVEIRA
Membro Titular - Examinador(a) Externo à Instituição - HELLEN MONCAO DE CARVALHO SANTANA
Membro Titular - Examinador(a) Externo à Instituição - EURÍPEDES CARVALHO DA SILVA - IFCE
Membro Titular - Examinador(a) Externo à Instituição - REGILENE OLIVEIRA
Membro Suplente - Examinador(a) Externo à Instituição - EWERTON ROCHA VIEIRA - UFG
Membro Suplente - Examinador(a) Externo à Instituição - RODRIGO MARTINS
Membro Suplente - Examinador(a) Externo à Instituição - GUIDO GERSON ESPIRITU LEDESMA - UERJ