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Search Results: 1 - 10 of 43984 matches for " Zhongtao Wu "
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Perturbed Floer Homology of some Fibered Three Manifolds II
Zhongtao Wu
Mathematics , 2009,
Abstract: Modifying the method of [21], we compute the perturbed $HF^+$ for some special classes of fibered three manifolds in the second highest spin$^c$-structures $S_{g-2}$. The special classes considered in this paper include the mapping tori of Dehn twists along a single non-separating curve and along a transverse pair of curves.
On mapping cones of Seifert fibered surgeries
Zhongtao Wu
Mathematics , 2011, DOI: 10.1112/jtopol/jts008
Abstract: Using the mapping cone of a rational surgery, we give several obstructions for Seifert fibered surgeries, including obstructions on the Alexander polynomial, the knot Floer homology, the surgery coefficient and the Seifert and four-ball genus of the knot.
Perturbed Floer Homology of some fibered three manifolds
Zhongtao Wu
Mathematics , 2008, DOI: 10.2140/agt.2009.9.337
Abstract: In this paper, we write down a special Heegaard diagram for a given product three manifold $\Sigma_g\times S^1$. We use the diagram to compute its perturbed Heegaard Floer homology.
Cosmetic Surgery in Integral Homology $L$-Spaces
Zhongtao Wu
Mathematics , 2009, DOI: 10.2140/gt.2011.15.1157
Abstract: Let $K$ be a non-trivial knot in $S^3$, and let $r$ and $r'$ be two distinct rational numbers of same sign, allowing $r$ to be infinite; we prove that there is no orientation-preserving homeomorphism between the manifolds $S^3_r(K)$ and $S^3_{r'}(K)$. We further generalize this uniqueness result to knots in arbitrary integral homology L-spaces.
A cabling formula for $ν^+$ invariant
Zhongtao Wu
Mathematics , 2015,
Abstract: We prove a cabling formula for the concordance invariant $\nu^+$, defined by the author and Hom. This gives rise to a simple and effective 4-ball genus bound for many cable knots.
Cosmetic surgeries on knots in $S^3$
Yi Ni,Zhongtao Wu
Mathematics , 2010,
Abstract: Two Dehn surgeries on a knot are called {\it purely cosmetic}, if they yield manifolds that are homeomorphic as oriented manifolds. Suppose there exist purely cosmetic surgeries on a knot in $S^3$, we show that the two surgery slopes must be the opposite of each other. One ingredient of our proof is a Dehn surgery formula for correction terms in Heegaard Floer homology.
Heegaard Floer correction terms and rational genus bounds
Yi Ni,Zhongtao Wu
Mathematics , 2012,
Abstract: Given an element in the first homology of a rational homology 3-sphere $Y$, one can consider the minimal rational genus of all knots in this homology class. This defines a function $\Theta$ on $H_1(Y;\mathbb Z)$, which was introduced by Turaev as an analogue of Thurston norm. We will give a lower bound for this function using the correction terms in Heegaard Floer homology. As a corollary, we show that Floer simple knots in L-spaces are genus minimizers in their homology classes, hence answer questions of Turaev and Rasmussen about genus minimizers in lens spaces.
Four-ball genus bounds and a refinement of the Ozsvath-Szabo tau-invariant
Jennifer Hom,Zhongtao Wu
Mathematics , 2014,
Abstract: Based on work of Rasmussen, we construct a concordance invariant associated to the knot Floer complex, and exhibit examples in which this invariant gives arbitrarily better bounds on the 4-ball genus than the Ozsvath-Szabo tau invariant.
Correction terms, $\mathbb Z_2$--Thurston norm, and triangulations
Yi Ni,Zhongtao Wu
Mathematics , 2014,
Abstract: We show that the correction terms in Heegaard Floer homology give a lower bound to the the genus of one-sided Heegaard splittings and the $\mathbb Z_2$--Thurston norm. Using a result of Jaco--Rubinstein--Tillmann, this gives a lower bound to the complexity of certain closed $3$--manifolds. As an application, we compute the $\mathbb Z_2$--Thurston norm of the double branched cover of some closed 3--braids, and give upper and lower bounds for the complexity of these manifolds.
Invariant metrics with nonnegative curvature on compact Lie groups
Nathan Brown,Rachel Finck,Matthew Spencer,Kristopher Tapp,Zhongtao Wu
Mathematics , 2004,
Abstract: We classify left invariant metrics with nonnegative curvature on SO(3) and U(2).
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