Algebraic, geometric, and differential topology

• Grant number: 22/16455-6
• Support Opportunities: Research Projects - Thematic Grants
• Start date: June 01, 2024
• End date: May 31, 2029
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Geometry and Topology
• Principal Investigator: Daciberg Lima Gonçalves
• Grantee: Daciberg Lima Gonçalves
• Host Institution: Instituto de Matemática e Estatística (IME). Universidade de São Paulo (USP). São Paulo , SP, Brazil
• City of the host institution: São Paulo
• Principal investigators: Edivaldo Lopes dos Santos ; Luiz Roberto Hartmann Junior ; Pedro Luiz Queiroz Pergher
• Associated researchers: Alexandre Paiva Barreto ; Alice Kimie Miwa Libardi ; Bartira Maues ; Behrooz Mirzaii ; Carlos Alberto Maquera Apaza ; Carlos Biasi ; Cesar Augusto Ipanaque Zapata ; Cynthia de Oliveira Lage Ferreira ; Dahisy Valadão de Souza Lima ; Dalton Couto Silva ; Daniel Vendrúscolo ; Denise de Mattos ; João Peres Vieira ; Ketty Abaroa de Rezende ; Leandro Vicente Mauri ; Marco Antonio de Freitas Contessoto ; Mariana Rodrigues da Silveira ; Natalia Andrea Viana Bedoya ; Oziride Manzoli Neto ; Thaís Fernanda Mendes Monis ; Thais Maria Dalbelo ; Thiago de Melo ; Wagner Carvalho Sgobbi
• Associated research grant(s): 24/19199-6 - Braid groups of the projective plane and Configuration orbit spaces, AP.R SPRINT
• Associated scholarship(s): 25/14696-4 - (Co)homological classes of continuous maps between manifolds and applications, BP.DR; 25/08629-2 - Equivariant cohomology theory and applications, BP.MS; 25/17280-3 - Introduction to Differential Geometry, BP.IC; + associated scholarships 25/20248-4 - Topics in Algebraic Topology: Homological Algebra, Singular Homology, and Applications, BP.IC; 24/22100-1 - Torsion invariants and finite transformations groups, BP.MS; 25/00534-2 - The homology of classical groups, BP.DR; 25/08260-9 - Differential Geometry of curves and surfaces in non euclidian spaces, BP.IC; 24/18154-9 - Fixed point theory via Algebraic Topology and Nilmanifolds, BP.MS; 24/17530-7 - Classical Topology Theorems, BP.IC; 24/09236-1 - Combinatorial invariants on stratified spaces, BP.DR; 24/14023-7 - Introduction to Morse Theory, BP.IC; 24/14246-6 - On the Bárány-Larman conjecture, Tverberg's theorem and related topics, BP.PD - associated scholarships

Abstract

This project is a continuation of the thematic projects 00/05385-8, 04/10229-6, 08/57607-6, 12/24454-8, 16/24707-4 and aims to develop research in Algebraic, Geometric and Differential Topology and Topological Data Analysis. The project consists in the training of human resources in the project's research lines, qualified scientific production and scientific visits both by foreign researchers as well as visits by Brazilian members abroad to institutions or outstanding researchers, congresses, seminars etc., providing conditions for a better performance and result for the development of the projects. (AU)

Scientific publications

(12)

(The scientific publications listed on this page originate from the Web of Science or SciELO databases. Their authors have cited FAPESP grant or fellowship project numbers awarded to Principal Investigators or Fellowship Recipients, whether or not they are among the authors. This information is collected automatically and retrieved directly from those bibliometric databases.)

DE REZENDE, KETTY A.; LIMA, DAHISY V. S.; ZIGART, MURILO A. DE JESUS. Gutierrez-Sotomayor flows: isolating blocks and homotopical cancellations. SAO PAULO JOURNAL OF MATHEMATICAL SCIENCES, v. 19, n. 1, p. 53-pg., 2025-06-01. (23/03430-8, 22/16455-6, 23/17645-6, 18/13481-0)

DA SILVA, VINICIUS BARROS; VIEIRA, JOAO PERES; LEONEL, EDSON DENIS. Exploring Limit Cycles of Differential Equations through Information Geometry Unveils the Solution to Hilbert's 16th Problem. Entropy, v. 26, n. 9, p. 73-pg., 2024-09-01. (22/16455-6, 21/09519-5, 19/14038-6)

ZAPATA, CESAR A. IPANAQUE; DE MATTOS, DENISE. Equivariant category and topological complexity of wedges. Glasgow Mathematical Journal, v. N/A, p. 20-pg., 2025-09-15. (22/16695-7, 18/23678-6, 23/16525-7, 16/18714-8, 22/16455-6)

BERTOLIM, MARIA A.; DE REZENDE, KETTY A.; MELLO, MARGARIDA P.. MINIMAL FLOW MORSIFICATION SUBJECT TO LEVEL SET CONTROL: A COMBINATORIAL APPROACH. TOPOLOGICAL METHODS IN NONLINEAR ANALYSIS, v. 65, n. 2, p. 55-pg., 2025-12-01. (22/16455-6, 18/13481-0)

GONCALVES, DACIBERG LIMA; LAASS, VINICIUS CASTELUBER; SILVA, WESLEM LIBERATO. The Borsuk-Ulam property for homotopy classes on bundles, parametrized braids groups and applications for surfaces bundles. Topology and its Applications, v. 359, p. 25-pg., 2024-12-16. (22/16455-6, 16/24707-4)

VIANA BEDOYA, NATALIA A.; GONCALVES, DACIBERG LIMA. Decomposability of minimal defect branched coverings over the projective plane. JOURNAL OF KNOT THEORY AND ITS RAMIFICATIONS, v. 34, n. 13, p. 30-pg., 2025-09-03. (22/16455-6)

DEKIMPE, KAREL; LIMA GONCALVES, DACIBERG; OCAMPO, OSCAR. The R_∞-property for braid groups over orientable surfaces. MONATSHEFTE FUR MATHEMATIK, v. N/A, p. 18-pg., 2025-07-07. (22/16455-6)

DE MELO, THIAGO; ROSA, RODRIGO; PEREIRA, JAMIL VIANA; MIO, WASHINGTON; VON ZUBEN, CLAUDIO JOSE; LIBARDI, ALICE KIMIE MIWA. Optimization of Maggot Mass Rearing via Topological Statistics Approach. BOLETIM SOCIEDADE PARANAENSE DE MATEMATICA, v. -43, p. 11-pg., 2025-01-01. (16/24707-4, 22/16455-6)

GONCALVES, D. L.; GONZALEZ, J.. Borsuk-Ulam Property for Graphs II: The Zn-Action. LOBACHEVSKII JOURNAL OF MATHEMATICS, v. 46, n. 3, p. 19-pg., 2025-03-01. (22/16455-6, 16/24707-4)

FENILLE, MARCIO COLOMBO; GONCALVES, DACIBERG LIMA. Twisted and Absolute Degrees of Maps into the Projective Plane. Acta Mathematica Sinica - English Series, v. 41, n. 5, p. 14-pg., 2025-05-01. (22/16455-6)

BRASSELET, JEAN-PAUL; LIMA, DAHISY V. S.; ZIGART, MURILO A. J.. Conley Index and Schwartz Index on Singular Surfaces. Qualitative Theory of Dynamical Systems, v. 24, n. 4, p. 27-pg., 2025-07-28. (23/17645-6, 22/16455-6, 23/03430-8, 19/21181-0)

GONSALVES, D. L.; LIBARDI, A. K. M.; VENDRUSCOLO, D.; VIEIRA, J. P.. On minimal fixed points set of fiber preserving maps of S1-bundles over S1. Topology and its Applications, v. 359, p. 13-pg., 2024-12-16. (22/16455-6, 16/24707-4)