# Fixed points of multimaps on surfaces with application to the torus- a Braid approach

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Date/heure
Date(s) - 20/10/2014
14 h 00 min - 15 h 00 min

Catégories Pas de Catégories

Let $\phi: S \to S$ be an $n-$valued continuous multimap on some closed
surface $S$. First we define the set of those maps called split. Then we
describe the set of homotopy classes of such multimaps where for most of
the surfaces the classification is given in terms of braids on $n-$strings
and the pure $n-$braids. The case where $S$ is either $S^2$ or
$RP^2$(projective plane) will be explained separately. For the case where the surface has genus > 0 then we give an algebraic
criterion to decide which homotopy classes of maps contains a
representative which is fixed point free. Despite
the fact that the algebraic condition is quite hard, we perform some
explicit calculation for the case where $S$ is the torus and explain the
sate of art of the problem in this case.

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