Algebraic, geometric and differential topology

• Grant number: 16/24707-4
• Support Opportunities: Research Projects - Thematic Grants
• Duration: June 01, 2017 - May 31, 2023
• 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
• Pesquisadores principais: Carlos Biasi ; Oziride Manzoli Neto ; Pedro Luiz Queiroz Pergher
• Associated researchers: Alexandre Paiva Barreto ; Alice Kimie Miwa Libardi ; Cynthia de Oliveira Lage Ferreira ; Dahisy Valadão de Souza Lima ; Daniel Vendrúscolo ; Denise de Mattos ; Dirceu Penteado ; Dirk Toeben ; Edivaldo Lopes dos Santos ; Eliris Cristina Rizziolli ; Ermínia de Lourdes Campello Fanti ; Évelin Meneguesso Barbaresco ; Flávia Souza Machado da Silva ; Irene Ignazia Onnis ; JAMIL VIANA PEREIRA ; João Peres Vieira ; José Eduardo Prado Pires de Campos ; Ketty Abaroa de Rezende ; Luiz Roberto Hartmann Junior ; Marcio Fuzeto Gameiro ; Marco Antonio de Freitas Contessoto ; Maria Gorete Carreira Andrade ; Mariana Rodrigues da Silveira ; Natalia Andrea Viana Bedoya ; Northon Canevari Leme Penteado ; Renata Zotin Gomes de Oliveira ; Sadao Massago ; Sergio Tsuyoshi Ura ; Thiago de Melo ; Tomas Edson Barros
• Associated grant(s): 19/20854-0 - Weingarten surfaces in R^3 and complete hypersurfaces with negative Ricci curvature in R^{n+1}, AV.BR
• Associated scholarship(s): 22/16430-3 - Homotopy classes of maps and minimal models for roots., BP.MS; 22/16695-7 - Sectional theory of a morphism, BP.PD; 23/02664-5 - Introduction to Analytic number theory, BP.IC; + associated scholarships 23/01101-7 - Primary obstruction to topological embeddings between manifolds, BP.MS; 22/08949-9 - Introduction to the Morse Theory, BP.IC; 22/07198-0 - Braids, configuration spaces and applications to multivalued maps, BP.PD; 22/03270-8 - Braids, configurations spaces and applications in multivalued maps, BP.PD; 21/09177-7 - Geometric analysis, Ricci flow and applications, BP.MS; 21/12689-0 - Algebraic Topology, tools and applications, BP.IC; 21/09540-4 - Heat kernel and analysis on riemannian manifolds, BP.IC; 21/02549-6 - Introduction to the study of braids and some applications related to links, BP.IC; 20/00814-1 - The study of the vector field problem for homogeneous spaces, BP.MS; 20/06159-5 - Root and homotopy theory, manifold topology, stratified spaces, spherical spacial forms and topological dynamical systems, BP.PD; 20/01077-0 - Topics on algebraic topology II, BP.IC; 19/26839-3 - Weingarten surfaces, BP.IC; 19/03998-9 - Introduction to hyperbolic geometry, BP.IC; 18/23410-3 - Topological complexity and Lusternik-Schnirelmann category, BP.MS; 18/23928-2 - Topological methods in combinatorics, Discrete Geometry and graph theory, BP.DR; 19/00623-4 - Simplicial homology and applications, BP.IC; 18/18592-5 - Introduction to algebraic topology, BP.IC; 18/17240-8 - Persistent Homology of functional data in aleatory metric spaces, BP.PD; 18/19603-0 - Homotopy and root theory, manifold theory, stratified spaces, spherical space forms and topological dynamic systems., BP.PD; 18/16414-2 - Introduction to the theory of minimal surfaces in R^3, BP.IC; 17/21208-0 - Geometric invariants of groups and property R-infinity., BP.DR; 18/04893-3 - Topics in algebraic topology: singular homology and applications, BP.IC; 18/08187-6 - Equivariant cobordism, Nielsen theory and applications., BP.PD; 17/19296-8 - An introduction to singular homology, BP.IC; 17/17864-9 - Toric actions, Euler obstruction and Brasselet number, BP.PD; 17/23101-8 - Minimal surfaces and the Weierstrass representation theorem, BP.IC; 17/14678-0 - Persistent homology generators and applications, BP.MS - associated scholarships

Abstract

This project consists in developing research in five areas which are part of Geometry/Topology and there exist active groups in the state of São Paulo. These groups work in (a) Fixed Point and Coincidence Theory; (b) Bordism $(Z_2)^k$-equivariante and Group Cohomology; (c) Topology of the Manifolds; (d) Bordism and Homotopy Theory; (e) Braid Groups; Topological data analysis. The problems to be studied in each sub-area represent relevant contribuition for the development of the sub-area. To exemplify: the study of the coincidence theory for spaces with different dimension, the study of braid groups of surfaces and braids on orbit spaces, $(Z_2)^k$ equivariant bordism, fixed point of involutions, properties of generalized manifolds, Borsuk-Ulam type theorems, torsion invariants, classification problems in geometric topology and cobordism, reconstruction of manifolds using barcodes and application of TDA to Biology. As part of the project is expected to have visitor and mainly that the participants of the projet can visit other instituitions abroad, collaborates, to participate in conference, workshop, etc., creating good conditions for the development of the project. As result of the proximity of the sub-areas many participants more close related to one project will also be interested in other groups. Finally we expect provide some computer facilities for some people which have need and is notable to obtain in a regular basis from their own institutions. (AU)

Scientific publications

(35)

(References retrieved automatically from Web of Science and SciELO through information on FAPESP grants and their corresponding numbers as mentioned in the publications by the authors)

MONTALDO, STEFANO; ONNIS, IRENE I.; PASSAMANI, APOENA PASSOS. Biharmonic constant mean curvature surfaces in Killing submersions. JOURNAL OF GEOMETRY AND PHYSICS, v. 133, p. 91-101, NOV 2018. (16/24707-4)

ONNIS, IRENE I.; PASSAMANI, APOENA PASSOS; PIU, PAOLA. Constant Angle Surfaces in Lorentzian Berger Spheres. JOURNAL OF GEOMETRIC ANALYSIS, v. 29, n. 2, p. 1456-1478, APR 2019. (16/24707-4)

GONCALVES, DACIBERG LIMA; DOS SANTOS, ANDERSON PAIAO. Diagonal Involutions and the Borsuk-Ulam Property for Product of Surfaces. BULLETIN OF THE BRAZILIAN MATHEMATICAL SOCIETY, v. 50, n. 3, p. 771-786, SEP 2019. (16/24707-4)

DE MATTOS, DENISE; DOS SANTOS, EDIVALDO L.; SILVA, NELSON ANTONIO. On the length of cohomology spheres. Topology and its Applications, v. 293, APR 15 2021. (16/24707-4, 11/23610-3)

GONCALVES, DACIBERG; SANKARAN, PARAMESWARAN; WONG, PETER. Twisted conjugacy in fundamental groups of geometric 3-manifolds. Topology and its Applications, v. 293, APR 15 2021. (16/24707-4)

GONCALVES, DACIBERG LIMA; GUASCHI, JOHN; OCAMPO, OSCAR; DE MIRANDA E PEREIRO, CAROLINA. Crystallographic groups and flat manifolds from surface braid groups. Topology and its Applications, v. 293, APR 15 2021. (16/24707-4)

GONCALVES, DACIBERG LIMA; GUASCHI, JOHN; OCAMPO, OSCAR. Almost-crystallographic groups as quotients of Artin braid groups. Journal of Algebra, v. 524, p. 160-186, APR 15 2019. (14/50131-7, 16/24707-4, 16/50354-1, 12/24454-8)

LIMA, D. V. S.; DA SILVEIRA, M. R.; VIEIRA, E. R.. Covering action on Conley index theory. Ergodic Theory and Dynamical Systems, v. N/A, p. 33-pg., 2022-02-21. (16/24707-4, 20/11326-8, 18/13481-0)

GONCALVES, DACIBERG LIMA; GUASCHI, JOHN; LAASS, VINICIUS CASTELUBER. THE BORSUK-ULAM PROPERTY FOR HOMOTOPY CLASSES OF MAPS FROM THE TORUS TO THE KLEIN BOTTLE PART 2. TOPOLOGICAL METHODS IN NONLINEAR ANALYSIS, v. 60, n. 2, p. 26-pg., 2022-12-01. (16/24707-4)

FENILLE, MARCIO COLOMBO; GONCALVES, DACIBERG LIMA; NETO, OZIRIDE MANZOLI. Strong surjections from two-complexes with odd order top-cohomology onto the projective plane. Journal of Fixed Point Theory and Applications, v. 25, n. 2, p. 13-pg., 2023-06-01. (16/24707-4)

DE MELO, GIVANILDO DONIZETI; VENDRUSCOLO, DANIEL. Nielsen-Borsuk-Ulam number for maps between tori. Journal of Fixed Point Theory and Applications, v. 25, n. 2, p. 21-pg., 2023-06-01. (16/24707-4)

LIMA, D. V. S.; DE REZENDE, K. A.; DA SILVEIRA, M. R.. Cancellations of periodic orbits for non-singular Morse-Smale flows. Ergodic Theory and Dynamical Systems, v. N/A, p. 49-pg., 2023-05-25. (18/13481-0, 16/24707-4, 20/11326-8)

GONCALVES, D.; NASYBULLOV, T.. Explicit solutions of certain orientable quadratic equations in free groups. INTERNATIONAL JOURNAL OF ALGEBRA AND COMPUTATION, v. 29, n. 8, p. 1451-1466, DEC 2019. (16/24707-4)

CADDEO, RENZO; ONNIS, IRENE I.; PIU, PAOLA. our's theorem and helicoidal surfaces with constant mean curvature in the Bianchi-Cartan-Vranceanu space. Annali di Matematica Pura ed Applicata, v. 201, n. 2, AUG 2021. (16/24707-4)

FANTI, E. L. C.; SILVA, L. S.. Some properties of E(G, W, F(T)G) and an application in the theory of splittings of groups. ALGEBRA & DISCRETE MATHEMATICS, v. 30, n. 2, p. 179-193, 2020. (12/24454-8, 16/24707-4)

PERGHER, PEDRO L. Q.; RAMOS, ADRIANA. Involutions Fixing Two Copies of Projective Spaces Under Different Rings. BULLETIN OF THE BRAZILIAN MATHEMATICAL SOCIETY, v. N/A, p. 9-pg., 2022-04-08. (16/24707-4)

DEKIMPE, KAREL; GONCALVES, DACIBERG LIMA. The R-infinity-property for nilpotent quotients of Baumslag-Solitar groups. Journal of Group Theory, v. 23, n. 3, p. 545-562, MAY 2020. (16/24707-4)

GONCALVES, DACIBERG LIMA; GUASCHI, JOHN; LAASS, VINICIUS CASTELUBER. Free Cyclic Actions on Surfaces and the Borsuk-Ulam Theorem. Acta Mathematica Sinica - English Series, v. 38, n. 10, p. 20-pg., 2022-10-01. (16/24707-4)

PAIVA, THALES FERNANDO VILAMAIOR; DOS SANTOS, EDIVALDO LOPES. Free involutions on odd dimensional Wall manifolds and cohomology of orbit spaces. Topology and its Applications, v. 314, p. 13-pg., 2022-05-10. (16/24707-4)

PAIVA, THALES FERNANDO VILAMAIOR; DOS SANTOS, EDIVALDO LOPES. Free circle actions on Dold and Wall manifolds. Topology and its Applications, v. 333, p. 9-pg., 2023-04-25. (16/24707-4)

GONCALVES, DACIBERG LIMA; MARTINS, SERGIO TADAO. The groups Aut and Out of the fundamental group of a closed Sol 3-manifold. JOURNAL OF ALGEBRA AND ITS APPLICATIONS, v. N/A, p. 29-pg., 2022-07-07. (16/24707-4, 12/24454-8, 13/07510-4)

FENILLE, MARCIO COLOMBO; GONCALVES, DACIBERG LIMA; PRADO, GUSTAVO DE LIMA. MINIMIZING ROOTS OF MAPS BETWEEN SPHERES AND PROJECTIVE SPACES IN CODIMENSION ONE. Proceedings of the American Mathematical Society, v. 150, n. 12, p. 10-pg., 2022-07-15. (16/24707-4)

CADDEO, RENZO; ONNIS, IRENE I.; PIU, PAOLA. Loxodromes on Invariant Surfaces in Three-Manifolds. Mediterranean Journal of Mathematics, v. 17, n. 1, FEB 2020. (16/24707-4)

BIASI, CARLOS; LIBARDI, ALICE K. M.; DE MELO, THIAGO; DOS SANTOS, EDIVALDO L.. Some results on extension of maps and applications. PROCEEDINGS OF THE ROYAL SOCIETY OF EDINBURGH SECTION A-MATHEMATICS, v. 149, n. 6, p. 1465-1472, DEC 2019. (16/24707-4)

BIASI, CARLOS; LIBARDI, ALICE KIMIE MIWA; DE MATTOS, DENISE; URA, SERGIO TSUYOSHI. Borsuk-Ulam theorem for filtered spaces. FORUM MATHEMATICUM, v. 33, n. 2, p. 419-426, MAR 2021. (16/24707-4, 18/17240-8)

LIMA, D. V. S.; RAMINELLI, S. A.; DE REZENDE, K. A.. HOMOTOPICAL CANCELLATION THEORY FOR GUTIERREZ-SOTOMAYOR SINGULAR FLOWS. JOURNAL OF SINGULARITIES, v. 23, p. 33-91, 2021. (14/11943-6, 18/13481-0, 15/10930-0, 16/24707-4)

PENTEADO, NORTHON CANEVARI LEME; NETO, OZIRIDE MANZOLI. REPRESENTING HOMOTOPY CLASSES BY MAPS WITH CERTAIN MINIMALITY ROOT PROPERTIES II. TOPOLOGICAL METHODS IN NONLINEAR ANALYSIS, v. 56, n. 2, p. 473-482, DEC 2020. (16/24707-4)

DEKIMPE, KAREL; GONCALVES, DACIBERG LIMA; OCAMPO, OSCAR. The R-infinity property for pure Artin braid groups. MONATSHEFTE FUR MATHEMATIK, v. 195, n. 1, FEB 2021. (16/24707-4)

BRASSELET, JEAN-PAUL; MIWA LIBARDI, ALICE KIMIE; RIZZIOLLI, ELIRIS CRISTINA; SAIA, MARCELO JOSE. Cobordism of maps of locally orientable Witt spaces. PUBLICATIONES MATHEMATICAE-DEBRECEN, v. 94, n. 3-4, p. 299-317, 2019. (14/00304-2, 16/24707-4, 15/06697-9)

GOLASINSKI, MAREK; GONCALVES, DACIBERG LIMA; WONG, PETER. On exponent and nilpotency of [Omega(Sr+1), Omega(KPn)]. Topology and its Applications, v. 293, APR 15 2021. (16/24707-4)

LIMA, D. V. S.; MANZOLI NETO, O.; DE REZENDE, K. A.. On handle theory for Morse-Bott critical manifolds. Geometriae Dedicata, v. 202, n. 1, p. 265-309, OCT 2019. (12/18780-0, 16/24707-4, 14/11943-6)

GONCALVES, DACIBERG LIMA; SANKARAN, PARAMESWARAN. Twisted conjugacy in PL-homeomorphism groups of the circle. Geometriae Dedicata, v. 202, n. 1, p. 311-320, OCT 2019. (16/24707-4)

GONCALVES, DACIBERG; SANKARAN, PARAMESWARAN; WONG, PETER. Twisted conjugacy in free products. COMMUNICATIONS IN ALGEBRA, v. 48, n. 9, APR 2020. (16/24707-4)

SGOBBI, WAGNER C.; SILVA, DALTON C.; VENDRUSCOLO, DANIEL. The R-8 property for nilpotent quotients of Generalized Solvable Baumslag-Solitar groups. Journal of Group Theory, v. N/A, p. 15-pg., 2023-01-31. (16/24707-4, 19/03150-0, 17/21208-0)

GONCALVES, DACIBERG L.; MONIS, THAIS F. M.; SPIEZ, STANISLAW. DEFICIENT AND MULTIPLE POINTS OF MAPS INTO A MANIFOLD. HOUSTON JOURNAL OF MATHEMATICS, v. 46, n. 4, p. 20-pg., 2020-01-01. (16/24707-4, 18/03550-5, 13/07936-1)