most recent 30 from http://mathoverflow.net 2013-05-21T09:27:37Z http://mathoverflow.net/feeds/user/18496 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/126016/do-different-dehn-fillings-produce-homeomorphic-3-manifolds yanqing 2013-03-30T14:01:34Z 2013-04-01T13:59:34Z

<p>Hi, everyone. I am interested in the dehn filling and Hyperbolic 3-manifold. </p> <p>Suppose M be an orientable compact 3-manifold with one torus boundary and int(M) admit a hyperbolic structure. Thurston proved that almost all the dehn fillings produced hyperbolic 3-manifolds. </p> <p>My question is:</p> <p>Among all the hyperbolic dehn fillings, is there possible that two different hyperbolic dehn fillings produce same 3-manifold, for some M? Is it true for all the one cusp hyperbolic 3-manifolds? </p> <p>If the answer to the question is positive, is there an theorem describing this thing?</p> <p>Any answer and reference are welcome! Thanks!</p>

http://mathoverflow.net/questions/117065/the-carrier-graph-and-heegaard-surface yanqing 2012-12-23T03:03:29Z 2013-03-02T13:52:26Z

<p>Let $M$ be orientable 3-manifold admitting a Heegaard splitting $V\cup_{S}W$.</p> <p>Let $X$ be a carrier graph of $M$ such that rank($X$)=rank($\pi_{1} M$). </p> <p>Note: A connected graph is called a carrier graph of $M$ if there is a map $f: X\rightarrow M$ such that $f: \pi_{1} X\rightarrow \pi_{1}M$ is surjective. And we call $f$ a carrier map of $X$.</p> <p>Thank Agol for comments. I have editted my questions again.</p> <p>Now I want to know</p> <p>If we fix the carrier graph$X$, is it possible that there is a carrier map $f$ of $X$, $f(X)\subset S$? Can we ask $f(X)$ to be embedded into $S$?</p> <p>Or more weakerly, Is there a pair of $(X,f)$ such that $X$ is a carrier graph of $M$ with rank(X)=rank($\pi_{1} M$) and $f(X)$ can be embedded into $S$?</p>

http://mathoverflow.net/questions/116345/the-action-of-torsion-of-mcgs-on-curve-complex yanqing 2012-12-14T04:06:43Z 2012-12-18T14:28:23Z

<p>Hi everyone. </p> <p>Let $S$ be a closed surface with genus at least 3, $\alpha, \beta$ be the two vertices of curve complex of $S$ such that $d_{\mathcal {C}(S)}(\alpha, \beta)\geq 3$. </p> <p>My question is </p> <p>Is there a non-trivial finite ordered element $f$ of $MCG(S)$ such that $f(\alpha)=\alpha$ and $f(\beta)=\beta$ in $\mathcal {C}(S)$?</p> <p>Thanks!</p>

http://mathoverflow.net/questions/116341/pure-mapping-class-group-and-mapping-class-group yanqing 2012-12-14T02:52:31Z 2012-12-14T03:27:18Z

<p>Hi, everyone. </p> <p>I am not sure it is proper to ask the following question on here. </p> <p>Let $S$ be a genus $g\geq 1$ surface with 2-puncture, i.e. genus $g$ closed surface with 2 points removed. And there is a compact surface $S_{1}\subset S$ such that $S-S_{1}$ consists of 2 once-punctured disk. </p> <p>Now in Farb and Margalit' book "A primer on mapping class groups ", they defined the $Mod(S_{1})$ and $PMod(S)$. </p> <p>My first question is </p> <p>Is it true that we can treat $PMod(S)$ as a subgroup of $Mod(S_{1})$?</p>

http://mathoverflow.net/questions/113892/the-action-of-periodic-map-on-the-complex-of-curves yanqing 2012-11-20T02:45:59Z 2012-11-21T00:43:54Z

<p>Hi, everyone. </p> <p>Assume $S$ is a genus at least 2 orientable closed surface. And there is a simplical complex defined on $S$ called Curve complex. </p> <p>It is well known that any automorphism of surface $S$ acts on curve complex $\mathcal {C}(S)$ isometrically.</p> <p>Now I want to know that</p> <p>For any periodic and irreducible automorphism $f: S\rightarrow S$, is there a connected subcomplex $W\subset \mathcal {C}(S)$ with infinite diameter such that $f(W)=W$?</p> <p>Staylor constructed such a $W$. Now there is a handlebody $H$ such that $\partial H=S$. Let $f$ be as above, $W$ be the disk complex of $H$.</p> <p>Now I wonder: </p> <p>Is it still possible that $f(W)=W$?</p>

http://mathoverflow.net/questions/111461/faraway-curves-in-surface yanqing 2012-11-04T13:24:48Z 2012-11-20T23:22:57Z

<p>Let $S$ be a compact orientable 2-surface with $\chi(X)\leq -3$. Y.Minsky and H.Masur proved that the curve complex of $X$ is $\delta$-hyperbolic and infinite. E.Klarreich (see also U.Hamenstadt) proved the Gromov boundary of the curve complex of $S$ is bijective to the collection of ending laminations. Denote the collection of ending laminations by $B$.</p> <p>Note: ending lamination implies that its complement in $S$ is a collection of (once-punctured) ideal polygons. </p> <p>My question is: Given a number $N$, is there possible that there is a collection of essential simple closed curves $Y=\{c_{\eta} \mid \eta\in B\}$ such that $d_{\mathcal {C}(S)}(c_{\eta}, c_{\zeta})\geq N$, for any $\eta, \zeta \in B$ and $\eta \neq \zeta$?</p>

http://mathoverflow.net/questions/112478/a-question-on-1-1-bridge-knot yanqing 2012-11-15T13:01:44Z 2012-11-15T19:39:44Z

<p>Hi, everyone. I am interested in the complement of (1,1) bridge knot in a lens space, $S^{3}$. Is there one (1,1) bridge knot in $S^{3}$ or lens space such that its complement is hyperbolic? </p> <p>Note: A knot $K$ in $S^{3}$ or Lens space is (1,1) if for the standard genus 1 Heegaard splitting of $S^{3}$ or lens space, $K$ intersects each solid torus only one arc which is boundary parallel.</p>

http://mathoverflow.net/questions/107730/pseudo-anosov-map-heegaard-splitting-hyperbolic-3-manfold yanqing 2012-09-21T01:52:38Z 2012-09-21T16:26:43Z

<p>Hi, I am interested in the relationship between the pseudo-anosov map and volume of the hyperbolic 3-manifold. </p> <p>Assume $H_{1}$ and $H_{2}$ are two handlebodies with $\partial H_{1}=\partial H_{2}=S$. </p> <p>Question 1:For any pseudo-anosov homeomorphism $\psi: S\rightarrow S$, if the $n\in N$ is large enough, is $M_{\psi^{n}}=H_{1}\cup_{\psi^{n}} H_{2}$ hyperbolic? </p> <p>Question 2:Given a pseudo-anosov map $\psi$, suppose $M_{\psi^{n}}=H_{1}\cup_{\psi^{n}} H_{2}$ is hyperbolic, for any $n\geq k$, where $k\in N$. How does the Vol(M) change when $n$ goes to infinity?</p>

http://mathoverflow.net/questions/102274/what-is-the-isometry-group-of-adv yanqing 2012-07-15T09:01:34Z 2012-07-15T09:01:34Z

<p>Let $V$ be a compressionbody. </p> <p>Annulus and disk complex $AD(V)$ is defined to be:</p> <p>Vertex: An istopy class of spanning annulus or an essential disk. </p> <p>Place an edge between two vertices if the two vertices are disjoint. </p> <p>Obivously, $AD(V)$ is an 1-dimensional simplicial complex. </p> <p>My question is :</p> <p>What is the isometry group of $AD(V)$? </p> <p>Note: I heard that S.Schleimer just proved the isometry group of disk complex is isometric to the mapping class group of handlebody $V$. </p>

http://mathoverflow.net/questions/100859/requiring-references yanqing 2012-06-28T12:54:32Z 2012-06-28T16:48:48Z

<p>Assume $V$ be a genus larger than 1 handlebody, $S=\partial_{+} V$.</p> <p>Denote $N$ be the normal closure of $MCG(V)$ in $MCG(S)$.</p> <p>Is there any material related to the quotient group $MCG(S)/N$ ? Thanks!</p>

http://mathoverflow.net/questions/86800/heegaard-splitting-of-covering-hyperbolic-manifold yanqing 2012-01-27T07:27:40Z 2012-04-04T02:19:32Z

<p>I am curious about how the Heegaard genus changes after a finite covering. </p> <p>Is there anyone constructing an closed hyperbolic 3-manifold $N$ such that </p> <p>the Heegaard genus of a finite covering of $N$ is less than the Heegaard genus of $N$? </p> <p>Thank you!</p> <p>Note: Heegaard genus of a 3-manifold means the minimal genus of all Heegaard splittings.</p>

http://mathoverflow.net/questions/84440/dehn-surgery-on-handlebody yanqing 2011-12-28T10:53:17Z 2011-12-30T16:17:00Z

<p>Assume $V$ is a handlebody and $C$ be a simple closed curve contained in the interior of $V$. As Sam said, there exists some simple closed curve such that every dehn surgery along it produces a handlebody. So I assume $C$ can not be isotopic to a simple closed curve in $\partial V$. </p> <p>Obviously, trivial dehn surgery along $C$ produces a handlebody. So My question is:</p> <p>Is there a different dehn surgery along $C$ which produces a handlebody? </p> <p>Can we classify all the dehn surgery along $C$ which produce handlebodies?</p>

http://mathoverflow.net/questions/81873/what-is-the-meaning-of-a-curve-c-representing-identity-in-fundamental-group yanqing 2011-11-25T12:17:06Z 2011-11-27T21:30:15Z

<p>Suppose $M$ is a closed 3-manifold, $C\subset M$ is a simple closed curve which represent identity in $\pi_{1}(M)$. Then $C$ bounds an immersed disk in $M$. </p> <p>My question is:</p> <p>When does it bound an imbedded disk in $M$? </p> <p>I don't know about it at all. If you have any reference, please tell me. Thank you!</p>

http://mathoverflow.net/questions/78760/are-there-replacements-for-the-curve-complex-that-make-up-for-its-weaknesses yanqing 2011-10-21T12:25:49Z 2011-10-24T12:30:25Z

<p>As far as I know, the most common structure of curves in surface is called the curve complex. John Hempel linked the curve complex and Heegaard Splitting and defined Heegaard Distance. There are lots of results about that, e.g., the work of Tseuyoshi Kobayashi, Ruifeng Qiu, Martin Scharlemann, Saul Schleimer, Maggy Tomova, Yair Minsky and so on.</p> <p>This structure has a weak point in that that you can not see any symmetry, and since it is not locally finite, we can not figure out the geodesic. My question is:</p> <blockquote> <p>Is there any other structure which can avoid the weak points?</p> </blockquote>

http://mathoverflow.net/questions/78551/why-delta-is-a-codimension-2-manifold yanqing 2011-10-19T08:30:23Z 2011-10-19T12:06:30Z

<p>As in symmetric space $Sym^{g}(\Sigma)$, $g\geq 2$, $\Delta$ is defined to be the diagonal space , i.e, for any element $x=(x_{1}, X_{2},...,x_{g})\in \Delta$, there are existing $x_{i}=x_{j}$, where $i\neq j$. So my question is why $\Delta$ is a codimension-2 manifold?<br> would you please write it down if no mind? Thank you?</p>

http://mathoverflow.net/questions/78195/why-h-1-sigma-cong-h-1symg-sigma yanqing 2011-10-15T07:53:17Z 2011-10-15T07:53:17Z

<p>In paper holomorphic disks and 3-manifold invariants, Ozsvath and Szabo connstruct two homeomoephisms $\mathcal {f} : H_{1}(\Sigma)\rightarrow H_{1}(Sym^{g}(\Sigma))$ and $\mathcal {g} : H_{1}(Sym^{g}(\Sigma))\rightarrow H_{1}(\Sigma)$. Then they says these two maps are inverses of each other. </p> <p>Sorry for my weak ability, I can not see how this work. So can somebody explain it, like what f or g maps the generator to ? And why these two maps are inverses of each other? Thank you.</p>

http://mathoverflow.net/questions/78017/maslov-index-in-heegaard-floer-homology yanqing 2011-10-13T12:25:18Z 2011-10-14T01:38:27Z

<p>Can anyone explain what is definition of maslov index in Heegaard Floer homology? I am puzzled> Thank you.,</p>

http://mathoverflow.net/questions/126016/do-different-dehn-fillings-produce-homeomorphic-3-manifolds/126185#126185 yanqing 2013-04-01T14:35:03Z 2013-04-01T14:35:03Z

@Hoffman, great answer! Thanks!

http://mathoverflow.net/questions/126016/do-different-dehn-fillings-produce-homeomorphic-3-manifolds/126023#126023 yanqing 2013-04-01T13:24:20Z 2013-04-01T13:24:20Z

@Kent, great! Thanks a lot!

http://mathoverflow.net/questions/126016/do-different-dehn-fillings-produce-homeomorphic-3-manifolds/126023#126023 yanqing 2013-04-01T08:48:51Z 2013-04-01T08:48:51Z

@Kent, Excellent answer! Is there a positive example for the question?

http://mathoverflow.net/questions/126016/do-different-dehn-fillings-produce-homeomorphic-3-manifolds yanqing 2013-04-01T01:06:56Z 2013-04-01T01:06:56Z

@Agol, yes! Do you know any about it?

http://mathoverflow.net/questions/117065/the-carrier-graph-and-heegaard-surface yanqing 2012-12-23T07:52:38Z 2012-12-23T07:52:38Z

@Agol. Yes, I hope it can be embedded.

http://mathoverflow.net/questions/116345/the-action-of-torsion-of-mcgs-on-curve-complex/116706#116706 yanqing 2012-12-19T14:24:44Z 2012-12-19T14:24:44Z

great, thank you for your explicit example.

http://mathoverflow.net/questions/116345/the-action-of-torsion-of-mcgs-on-curve-complex/116357#116357 yanqing 2012-12-15T02:06:01Z 2012-12-15T02:06:01Z

@Misha. It is great. Thanks again!

http://mathoverflow.net/questions/116345/the-action-of-torsion-of-mcgs-on-curve-complex/116357#116357 yanqing 2012-12-14T12:11:05Z 2012-12-14T12:11:05Z

Well done, thanks!

http://mathoverflow.net/questions/116345/the-action-of-torsion-of-mcgs-on-curve-complex yanqing 2012-12-14T06:11:48Z 2012-12-14T06:11:48Z

@Agol, the last one.

http://mathoverflow.net/questions/113892/the-action-of-periodic-map-on-the-complex-of-curves yanqing 2012-11-21T00:34:46Z 2012-11-21T00:34:46Z

@HW: I don't want the $W$ is equal to the curve complex.

http://mathoverflow.net/questions/111461/faraway-curves-in-surface/113999#113999 yanqing 2012-11-21T00:25:54Z 2012-11-21T00:25:54Z

Great, thanks very much

http://mathoverflow.net/questions/113892/the-action-of-periodic-map-on-the-complex-of-curves/113904#113904 yanqing 2012-11-20T06:20:24Z 2012-11-20T06:20:24Z

@Agol: I have edited it again.

http://mathoverflow.net/questions/113892/the-action-of-periodic-map-on-the-complex-of-curves/113904#113904 yanqing 2012-11-20T05:52:48Z 2012-11-20T05:52:48Z

@Agol Since I required that $f$ is not reducible, $f$ can not fix any vertex on $\mathcal {C}(S)$.

http://mathoverflow.net/questions/111461/faraway-curves-in-surface/111597#111597 yanqing 2012-11-20T05:44:17Z 2012-11-20T05:44:17Z

@ staylor, great.

http://mathoverflow.net/questions/113892/the-action-of-periodic-map-on-the-complex-of-curves yanqing 2012-11-20T05:37:25Z 2012-11-20T05:37:25Z

@R.Kent I have edited it again.