Magdalena Georgescu, University of Victoria
"Characterization of spectral flow in a type II factor"
In
B(H)
(the
set
of
bounded
operators
on
a
Hilbert
space),
the
spectral
flow
counts
the
net
number
of
eigenvalues
which
change
sign
as
one
travels
along
a
path
of
self-adjoint
Fredholm
operators.
The
ability
to
calculate
the
spectral
flow
allows
one
to
calculate
the
Fredholm
index
of
some
operators,
making
it
of
interest
in
the
study
of
noncommutative
geometry.
It
is
possible
to
generalize
the
concept
of
spectal
flow
to
a
semifinite
von
Neumann
algebra,
as
we
can
use
a
trace
on
the
algebra
to
measure
the
amount
of
spectrum
which
changes
sign.
Lesch
showed
in
the
type
I
case
(i.e.
B(H))
that
a
map
on
a
suitable
set
of
paths
which
satisfies
three
fairly
straight-forward
conditions
is
the
spectral
flow
map.
In
this
talk,
I
will
describe
how
Lesch's
ideas
can
be
modified
to
obtain
a
characterization
of
spectral
flow
in
a
type
II
factor.