Diagonal maps and cohomology rings of sol manifolds and virtually cyclic groups

• Grant number: 13/21394-7
• Support Opportunities: Scholarships abroad - Research Internship - Post-doctor
• Start date: February 15, 2014
• End date: August 14, 2014
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Geometry and Topology
• Principal Investigator: Daciberg Lima Gonçalves
• Grantee: Sérgio Tadao Martins
• Supervisor: Ross Geoghegan
• Host Institution: Instituto de Matemática e Estatística (IME). Universidade de São Paulo (USP). São Paulo , SP, Brazil
• Institution abroad: Binghamton University, United States
• Associated to the scholarship: 13/07510-4 - Resolutions and the group cohomology of the sapphire manifolds and of the virtually cyclic groups, BP.PD

Abstract

The project consists in the study of two problems: the first is that of determining the cohomology of certain 3-manifolds known as torus semi-bundles, which admit the Sol geometry. The second problem is that of computing the cohomology rings of the virtually cyclic groups, motivated by the fact that such groups act on homotopy spheres. (AU)

Scientific publications

(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; MARTINS, SERGIO TADAO. Diagonal approximation and the cohomology ring of the fundamental groups of surfaces. EUROPEAN JOURNAL OF MATHEMATICS, v. 1, n. 1, p. 122-137, MAR 2015. (13/21394-7, 13/07510-4)

MARTINS, SERGIO TADAO. Diagonal approximation and the cohomology ring of torus fiber bundles. INTERNATIONAL JOURNAL OF ALGEBRA AND COMPUTATION, v. 25, n. 3, p. 493-530, MAY 2015. (13/21394-7, 13/07510-4)

GONCALVES, DACIBERG LIMA; MARTINS, SERGIO TADAO. The cohomology ring of the sapphires that admit the Sol geometry. INTERNATIONAL JOURNAL OF ALGEBRA AND COMPUTATION, v. 28, n. 3, p. 365-380, MAY 2018. (13/21394-7, 13/07510-4)