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Surjective homomorphisms between surface braid groups
Let be the pure braid group of a genus surface with
punctures. In this paper we prove that any surjective homomorphism
factors through one of the forgetful
homomorphisms. We then compute the automorphism group of ,
extending Irmak, Ivanov and McCarthy's result to the punctured case.
Surprisingly, in contrast to the case, any automorphism of
, is geometric.Comment: 12 pages, changes on writin
Partitions of the polytope of Doubly Substochastic Matrices
In this paper, we provide three different ways to partition the polytope of
doubly substochastic matrices into subpolytopes via the prescribed row and
column sums, the sum of all elements and the sub-defect respectively. Then we
characterize the extreme points of each type of convex subpolytopes. The
relations of the extreme points of the subpolytopes in the three partitions are
also given
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