Algebraic, geometric and differential topology

• Grant number: 04/10229-6
• Support Opportunities: Research Projects - Thematic Grants
• Start date: February 01, 2005
• End date: January 31, 2009
• 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: Pedro Luiz Queiroz Pergher

Abstract

This project consists in developing research in four areas which are part of Geometry/Topology and there exists active group-s in the State of São Paulo. These groups work in: a) fixed Point and Coincidence Theory; b) Bordismo (Z2)k-equivariant and group cohornology; c) Topology of the Manifolds, Bordismo and Homotopy Theory; d) Homotopy, Fibration and Gauge theory. The problems to be studied in each sub-area represent relevant contribution for the development of the sub area. To exemplify, in case a) we have the question of extending the coincidence theory for spaces with different dimension and the study of surface braid groups. In case b) to develop the theory of (Z2)k- equivariant bordism and group cohomology. In case c) to study topological embedding and monomorphism between vector space. In case d) the homology of the Gauge group of unitary bundle over a four dimension manifold and homtopy class of maps between quaernionic spaces. As part of the project it is expected to have visitor and mainly that the participants of the project can visit other institutions 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 to 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

(7)

(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)

GONCALVES, DACIBERG LIMA; GUASCHI, JOHN. Classification of the virtually cyclic subgroups of the pure braid groups of the projective plane. Journal of Group Theory, v. 13, n. 2, p. 277-294, MAR 2010. (04/10229-6)

GONÇALVES‚ D.; RANDALL‚ D.. Self-coincidence of mappings between spheres and the strong Kervaire invariant one problem. COMPTES RENDUS MATHEMATIQUE, v. 342, n. 7, p. 511-513, 2006. (04/10229-6)

GONÇALVES‚ D.L.. The Borsuk-Ulam theorem for surfaces. Quaestiones Mathematicae, v. 29, n. 1, p. 117-123, 2006. (04/10229-6)

GONÇALVES‚ DL; LIBARDI‚ A; MANZOLI, O. Some results on vector bundle monomorphisms. Algebraic and Geometric Topology, v. 7, p. 829-843, 2007. (04/10229-6)

BERTOLIM‚ M.A.; REZENDE‚ K.A.; NETO‚ O.M.; VAGO‚ G.M.. Isolating blocks for Morse flows. Geometriae Dedicata, v. 121, n. 1, p. 19-41, 2006. (04/10229-6)

DE MATTOS, DENISE; DOS SANTOS, EDIVALDO L.. ON NONSYMMETRIC THEOREMS FOR (H, G)-COINCIDENCES. TOPOLOGICAL METHODS IN NONLINEAR ANALYSIS, v. 33, n. 1, p. 105-119, MAR 2009. (04/10229-6)

CASAGRANDE, R.; DE REZENDE, K. A.; TEIXEIRA, M. A.. The Conley index for discontinuous vector fields. Geometriae Dedicata, v. 136, n. 1, p. 47-56, OCT 2008. (02/10246-2, 04/10229-6)