Yoshikata Kida
The co-Hopfian property of surface braid groups.
Втр, 06/15/2010 - 15:01 — SomNambulAuthors: Yoshikata Kida, Saeko Yamagata
Subjects: Group Theory
AbstractWhen both g and p are integers at least two, we give a description of any
injective homomorphism from a finite index subgroup of the braid group with p
strings on a closed orientable surface of genus g, into the braid group. As a
consequence, we show that any finite index subgroup of the braid group is
co-Hopfian.Injections of the complex of separating curves into the Torelli complex.
Пнд, 11/23/2009 - 16:01 — SomNambulAuthors: Yoshikata Kida
Subjects: Group Theory
AbstractWe show that for most of compact orientable surfaces, any superinjective map
from the complex of separating curves into the Torelli complex is induced from
an element of the extended mapping class group. As an application, we prove
that any injective homomorphism from a finite index subgroup of the Johnson
kernel into the Torelli group for such a surface is induced from an element of
the extended mapping class group.The co-Hopfian property of the Johnson kernel and the Torelli group.
Пнд, 11/23/2009 - 16:01 — SomNambulAuthors: Yoshikata Kida
Subjects: Group Theory
AbstractFor most of compact orientable surfaces, we show that any superinjective map
from the complex of separating curves into itself is induced from an element of
the extended mapping class group. We apply this result to proving that any
finite index subgroup of the Johnson kernel is co-Hopfian. The same properties
are shown for the Torelli complex and the Torelli group.Automorphisms of the Torelli complex and the complex of separating curves.
Пнд, 09/28/2009 - 15:24 — SomNambulAuthors: Yoshikata Kida
Subjects: Group Theory
AbstractWe compute the automorphism groups of the Torelli complex and the complex of
separating curves for most of compact orientable surfaces. As an application,
we show that the commensurators of the Torelli group and the Johnson kernel for
such surfaces are naturally isomorphic to the extended mapping class group.
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