Wednesday, February 13, 2019 3:30 pm
-
3:30 pm
EST (GMT -05:00)
Sanaz Pooya, Stockholm University
"On the Baum-Connes assembly map for certain semi-direct products"
The
Baum-Connes
conjecture
for
a
group
$G$
predicts
that
the
assembly
map
$
\mu^G_i\colon
\mathrm{K_i^G}(\underline{\mathrm
E}G)\rightarrow
\mathrm
{K_i}(C_{\mathrm
r}^*G)
$
is
an
isomorphism
for
$
i=0,
1$.
A
breakthrough
result
of
Higson
and
Kasparov
shows
that
a-T-menable
groups
satisfy
the
conjecture,
hence
the
group
$G
=
F\wr
\mathbb
F_n$,
where
$F$
is
finite
and
$\mathbb
F_n$
is
a
free
group.
This
result
however
does
not
describe
the
K-groups.
In
this
talk,
we
shed
light
on
the
assembly
map
for
this
group
and
describe
it
explicitly.
In
doing
so
we
reprove
the
conjecture
for
this
group.
MC 5417