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bio website math.princeton.edu/~ssivek
location Princeton, NJ
age 31
visits member for 5 years, 10 months
seen 7 hours ago

I'm a postdoc in low-dimensional topology at Princeton.


Jul
30
comment Surgery along an arc connecting the components of a $2$-component link gives the unknot
It's certainly used in the paper by Bao. I didn't see how the other papers use it to prove their results about band sums, although Eudave-Muñoz does invoke it afterward to apply his result to the cabling conjecture.
Jul
30
answered Surgery along an arc connecting the components of a $2$-component link gives the unknot
Jul
25
comment contact manifolds dimension five
Done, unless you had any other developments in mind.
Jul
25
revised contact manifolds dimension five
Added links to recent developments
Jul
23
comment Legendrian knot in 3-sphere
@nikita: The adjunction inequality says that $tb(L)\le 2g_*(L)-1$, so equality is still possible, but either way if you have a symplectic surface then it actually satisfies an adjunction formula $\langle c_1(\omega), \Sigma\rangle + \Sigma\cdot\Sigma = 2g(\Sigma)-2$. In response to your second comment, if the surface is symplectic then its branched double cover is naturally a symplectic manifold and so the contact structure which comes from taking the branched double cover of the transverse knot in S^3 is in fact symplectically fillable.
Jul
23
answered Legendrian knot in 3-sphere
Jul
9
comment Concrete examples of covering from the 3-torus to the 3-sphere
The 3-torus can't be a branched double cover because the triple cup product on $H^1$ would then be zero.
Feb
6
comment Regularity of the taut foliation
See "Approximating C^0-foliations" by Kazez and Roberts (arxiv.org/abs/1404.5919), which addresses exactly this issue.
Jan
12
answered Are there spaces in which there are no fibered knots?
Oct
16
awarded  Yearling
Jul
8
answered Do Heegaard Floer homology detect fibred knot in general oriented 3-manifold?
Jun
13
comment Heegaard Floer Homology of double branched cover
There are actually lots of non-QA knots whose branched double covers are L-spaces. See section 6.1 of arxiv.org/pdf/1205.5261.pdf for some discussion and explicit examples, including the $P(p_1,\dots,p_n,-q) $ pretzel knots where $p_i,q>0$ and $q = \min(p_1,\dots,p_n)$.
Mar
26
awarded  Guru
Dec
17
awarded  Enlightened
Dec
17
awarded  Nice Answer
Nov
21
comment Link surgery on $S^2\times S^1$
For n=2 you do have a product link. You can see it by writing the pages $(S^1\times I)$ of the open book collectively as $(S^1 \times I) \times S^1$, and then gluing in two solid tori $S^1\times D^2$ by using the disks $\{*\} \times D^2$ to cap off the annuli $(\{*\} \times I) \times S^1$ (which consist of one arc from each page). Thus in the surgered manifold the annuli $(\{*\}\times I)\times S^1$ can be closed up to form spheres $\{*\}\times S^2$, one for each point of $S^1$, and the link $L_2$ contributes a pair of points to each of those spheres.
Nov
21
comment Link surgery on $S^2\times S^1$
The argument only works for $n>0$ because when $n=0$ it isn't really an open book decomposition anymore, and then you really do have $S^2\times S^1$. You can check the n=2 case directly by Kirby calculus, though: it's 0-surgery on an unknot and on two of its meridians, and if you blow up one of those meridians you get a chain of unknots with surgery coefficients -1,-1,0,0. Blow down the second to get a chain with coefficients 0,1,0, and then the middle one, and then either of the remaining ones and you're left with a single 0-framed unknot, which gives $S^1\times S^2$.
Nov
21
answered Link surgery on $S^2\times S^1$
Oct
16
awarded  Yearling
Jul
9
awarded  Nice Answer