[0805.0583] Homotopy of unitaries in simple C*-algebras with tracial rank one
Let . Is there
satisfying the following? Given any pair of unitaries
and
in a unital separable simple C*-algebra
for which
, there is a continuous path of unitaries
such that
,
and
for all
. We give an answer to this question when
is assumed to be a unital simple C*-algebra with tracial rank no more than one.
Let be a unital separable simple C*-algebra, with tracial rank no more than one. Suppose that
is a unital monomorphism and
is a unitary such that
almost commutes with
. We give an answer to the question when there is a continuous path of unitaries
with
and
such that entire path
almost commute with
. Other versions of so-called basic homotopy lemma are also presented.