bio | website | math.princeton.edu/~ssivek |
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location | Princeton, NJ | |
age | 30 | |
visits | member for | 5 years, 1 month |
seen | Jul 20 at 19:37 | |
stats | profile views | 1,400 |
I'm a postdoc in low-dimensional topology at Princeton.
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 |
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 |