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This article is available for purchase or by subscription. See below.
Abstract
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The (untwisted) oriented cube of resolutions for knot Floer homology assigns a complex
to a singular
resolution
of a knot
. Manolescu conjectured
that when
is in braid
position, the homology
is isomorphic to the
homfly-pt homology of
.
Together with a naturality condition on the induced edge maps, this
conjecture would prove the existence of a spectral sequence from
homfly-pt
homology to knot Floer homology. Using a basepoint filtration on
,
a recursion formula for
homfly-pt homology and additional
–like
differentials on
,
we prove Manolescu’s conjecture. The naturality condition remains open.
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Keywords
knot theory, knot Floer, Khovanov–Rozansky, HOMFLY-PT,
homology
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Mathematical Subject Classification 2010
Primary: 57M27
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Publication
Received: 29 June 2017
Revised: 14 April 2018
Accepted: 23 April 2018
Published: 11 December 2018
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