1,446 research outputs found
L-spaces, taut foliations, and graph manifolds
If is a closed orientable graph manifold, we show that admits a
coorientable taut foliation if and only if is not an L-space. Combined with
previous work of Boyer and Clay, this implies that is an L-space if and
only if is not left-orderable.Comment: 10 pages, 1 figure; version 3 is accepted version, to appear in
Compositio Mathematic
On stable Khovanov homology of torus knots
We conjecture that the stable Khovanov homology of torus knots can be
described as the Koszul homology of an explicit non-regular sequence of
quadratic polynomials. The corresponding Poincare series turns out to be
related to the Rogers-Ramanujan identity.Comment: 28 page
Odd Khovanov homology
We describe an invariant of links in the three-sphere which is closely
related to Khovanov's Jones polynomial homology. Our construction replaces the
symmetric algebra appearing in Khovanov's definition with an exterior algebra.
The two invariants have the same reduction modulo 2, but differ over the
rationals. There is a reduced version which is a link invariant whose graded
Euler characteristic is the normalized Jones polynomial.Comment: 16 pages, 12 figure
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