Probabilistic and algebraic aspects of smooth dynamical systems
Transcendental methods of algebraic/complex geometry in hyperbolic geometry
Classic geometries and the construction of hyperbolic manifolds
Grant number: | 12/13615-0 |
Support Opportunities: | Scholarships in Brazil - Post-Doctorate |
Effective date (Start): | December 01, 2012 |
Effective date (End): | November 30, 2014 |
Field of knowledge: | Physical Sciences and Mathematics - Mathematics - Geometry and Topology |
Principal Investigator: | André Salles de Carvalho |
Grantee: | Rupert William Venzke |
Host Institution: | Instituto de Matemática e Estatística (IME). Universidade de São Paulo (USP). São Paulo , SP, Brazil |
Associated research grant: | 11/16265-8 - Low dimensional dynamics, AP.TEM |
Abstract We study a partial order on surface automorphisms called the "forcing order" that measures relative complexity of maps from a dynamical perspective. While the order can be difficult to compute directly when pseudo-Anosov growth is large, our previous work has succeeded in identifying the low growth braids. Using known results/conjectures about this order for Horseshoe braids, we would like to extend our understanding to the more general setting (working with low growth braids as a test case). The partial order extends to a partial order on (fibered) 3-manifolds and gives insight into the structure of invariants for hyperbolic 3-manifolds, such as volumes and homologies. Our hope is to additionally develop nice formulas for these invariants relative to standard models for realizing 3-manifolds, with the intention of classifying non-trivial families of 3-manifolds. | |
News published in Agência FAPESP Newsletter about the scholarship: | |
TITULO | |
Articles published in other media outlets (0 total): | |
More itemsLess items | |
VEICULO: TITULO (DATA) | |
VEICULO: TITULO (DATA) | |