- journal article metadata
European Mathematical Society Publishing House
2016-09-19 17:05:39
Quantum Topology
Quantum Topol.
QT
1663-487X
1664-073X
General
10.4171/QT
http://www.ems-ph.org/doi/10.4171/QT
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European Mathematical Society Publishing House
Zuerich, Switzerland
© European Mathematical Society
5
2014
2
An untwisted cube of resolutions for knot Floer homology
Ciprian
Manolescu
UCLA, LOS ANGELES, UNITED STATES
Knots, knot Floer homology, Khovanov–Rozansky homology, spectral sequences
Ozsváth and Szabó gave a combinatorial description of knot Floer homology based on a cube of resolutions, which uses maps with twisted coefficients. We study the $t=1$ specialization of their construction. The associated spectral sequence converges to knot Floer homology, and we conjecture that its $E_1$ page is isomorphic to the HOMFLY-PT chain complex of Khovanov and Rozansky. At the level of each $E_1$ summand, this conjecture can be stated in terms of an isomorphism between certain Tor groups. As evidence for the conjecture, we prove that such an isomorphism exists in degree zero.
Manifolds and cell complexes
General
185
223
10.4171/QT/50
http://www.ems-ph.org/doi/10.4171/QT/50