| Grant number: | 14/50131-7 |
| Support Opportunities: | Regular Research Grants |
| Start date: | April 01, 2014 |
| End date: | March 31, 2016 |
| Field of knowledge: | Physical Sciences and Mathematics - Mathematics - Geometry and Topology |
| Agreement: | CNRS |
| Principal Investigator: | Daciberg Lima Gonçalves |
| Grantee: | Daciberg Lima Gonçalves |
| Principal researcher abroad: | John Guaschi |
| Institution abroad: | Université de Caen Basse-Normandie, France |
| Host Institution: | Instituto de Matemática e Estatística (IME). Universidade de São Paulo (USP). São Paulo , SP, Brazil |
| Associated research grant: | 12/24454-8 - Algebraic, geometric and differential topology, AP.TEM |
Abstract
Our project is concerned with algebraic & topological properties of configuration spaces & braid groups, notably those of the disc D^2, the sphere S^2& the projective plane RP^2, some generalizations, such as orbit configuration spaces, & the relations of these braid groups with the classical crystallographic groups. The braid groups & their generalizations have attracted much attention, partly due to the fact that these groups arise in various contexts (topology, knot theory, algebra) Our proposal focusses on 3 different aspects: the homotopy fibres of inclusions of the configuration spaces of S ^2 & RP^2 in the Cartesian product, and orbit configuration spaces; the conjugacy classes of the finite subgroups of the braid groups of RP^2; & the relations between the braid groups of D^2, S^2, RP^2 and crystallographic groups. We will study these problems using algebra, algebraic topology, topology geometry. The results should have consequences for the associated mapping class groups. (AU)
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