We show that a decorated knot
concordance
from
to induces a
homomorphism
on knot Floer homology that preserves the Alexander and Maslov
gradings. Furthermore, it induces a morphism of the spectral sequences to
that agrees
with
on the
page and is the
identity on the
page.
It follows that
is
nonvanishing on
.
We also obtain an invariant of slice disks in homology 4–balls
bounding .
If is
invertible, then
is injective, hence
for every .
This implies an unpublished result of Ruberman that if there is an invertible concordance
from the knot
to ,
then
,
where denotes the Seifert
genus. Furthermore, if
and is fibred,
then so is .
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