4,096 reputation
12123
bio website math.princeton.edu/~ssivek
location Princeton, NJ
age 30
visits member for 4 years, 10 months
seen Jul 20 at 19:37

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


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
Jul
3
awarded  Informed
Jun
26
awarded  Enlightened
Jun
26
awarded  Nice Answer
Jun
25
awarded  Citizen Patrol
Jun
5
answered {0,1} Maslov potentials on Legendrian knots
Jun
4
answered Is every quasipositive knot strongly quasipositive?
Mar
4
awarded  Good Answer
Mar
4
awarded  Enlightened
Mar
3
awarded  Nice Answer
Mar
3
answered Are there non-compact, non-smoothable manifolds?