Yi Ni
Homological actions on sutured Floer homology.
Fri, 10/15/2010 - 15:01 — SomNambulAuthors: Yi Ni
Subjects: Geometric Topology
AbstractWe define the action of the homology group $H_1(M,\partial M)$ on the sutured
Floer homology $SFH(M,\gamma)$. It turns out that the contact invariant
$EH(M,\gamma,\xi)$ is usually sent to zero by this action. This fact allows us
to refine an earlier result proved by Ghiggini and the author. As a corollary,
we classify knots in $#^n(S^1\times S^2)$ which have simple knot Floer homology
groups: They are essentially the Borromean knots.Cosmetic surgeries on knots in $S^3$.
Mon, 09/27/2010 - 15:01 — SomNambulAuthors: Zhongtao Wu, Yi Ni
Subjects: Geometric Topology
AbstractTwo Dehn surgeries on a knot are called {\it purely cosmetic}, if they yield
manifolds that are homeomorphic as oriented manifolds. Using Heegaard Floer
homology, we give necessary conditions for the existence of purely cosmetic
surgeries on knots in $S^3$. Among other things, we show that the two surgery
slopes must be the opposite of each other.Dehn surgeries on knots in product manifolds.
Fri, 01/29/2010 - 16:01 — SomNambulAuthors: Yi Ni
Subjects: Geometric Topology
AbstractWe show that if a surgery on a knot in a product sutured manifold yields the
same product sutured manifold, then this knot is a 0-- or 1--crossing knot. The
proof uses techniques from sutured manifold theory.Thurston norm and cosmetic surgeries.
Mon, 01/25/2010 - 16:01 — SomNambulAuthors: Yi Ni
Subjects: Geometric Topology
AbstractTwo Dehn surgeries on a knot are called cosmetic if they yield homeomorphic
manifolds. For a null-homologous knot with certain conditions on the Thurston
norm of the ambient manifold, if the knot admits cosmetic surgeries, then the
surgery coefficients are equal up to sign.
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