Height functions on symmetric spaces
 
 
Description: 
Morse theory gives us useful techniques to analyze the homotopic structure of a smooth manifold studying some smooth functions on this manifold. This allows us to find the cellular structure of a CW-complex and get some information about its cohomology.
 
We will consider here height functions on symmetric spaces M=G/K embedded in the associated matrix Lie group G. There is no systematic characterization of Morse theory in this set. In fact, the results for Lie groups led in the past to study only height functions with the ground hyperplane orthogonal to a real diagonal matrix. We will analyze the relationship between the critical sets of the height function on G and its restriction to M. Also we will prove that the gradient flow on M can be integrated by means of a generalized Cayley transform; this allows us to obtain explicit local charts for the critical submanifolds. 
Date:  2015-07-09
Start Time:   15:00
Speaker:  María José Pereira-Sáez (Univ. Coruña, Spain)
Institution:  Universidade da Coruña, Spain
Place:  Sala 5.5
Research Groups: -Geometry
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