User li yu - MathOverflow most recent 30 from http://mathoverflow.net 2013-06-18T21:04:14Z http://mathoverflow.net/feeds/user/27253 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/128876/automorphism-of-a-lie-group-which-preserves-a-maximal-torus-is-necessarily-an-inn Automorphism of a Lie group which preserves a maximal torus is necessarily an inner automorphism? Li Yu 2013-04-27T00:05:56Z 2013-04-27T00:05:56Z <p>Let $G$ be a connected Lie group with a maximal torus $T$. Suppose $\sigma$ is an automorphism of $G$ so that $\sigma(T)=T$. Then can we conclude that $\sigma$ is an inner automorphism of $G$? (i.e. is there an element $g\in G$ so that $\sigma= Ad_g : G\rightarrow G$). </p> http://mathoverflow.net/questions/128788/normal-subgroup-of-the-identity-component-of-a-linear-lie-group-is-normal-in-the Normal subgroup of the identity component of a linear Lie group is normal in the whole group? Li Yu 2013-04-26T02:14:31Z 2013-04-26T02:44:40Z <p>Suppose $G$ is a linear Lie group (i.e. $G$ admits a finite dimensional faithful representation) and $G$ has finitely many connected components. Let $G_0$ be the identity component of $G$. If $N$ is a normal subgroup of $G_0$, is $N$ necessarily normal in $G$?</p> http://mathoverflow.net/questions/127313/description-of-the-units-of-the-group-ring-fpfp Description of the units of the group ring Fp[Fp] ? Li Yu 2013-04-12T03:58:16Z 2013-04-12T04:32:47Z <p>Is there a good way to see what the units of the group ring $\mathbb{F}_p[\mathbb{F}_p]$ (p is a prime) are? </p> http://mathoverflow.net/questions/126775/do-nielsen-transformations-on-a-presentation-preserve-the-homotopy-type-of-the-co Do Nielsen transformations on a presentation preserve the homotopy type of the corresponding presentation complex? Li Yu 2013-04-07T14:13:42Z 2013-04-07T21:06:39Z <p>Let $\mathcal{P}$ be a finite presentation of some group. When we apply some Nielsen transformations on $\mathcal{P}$, will the homotope type of the presentation complex $K_{\mathcal{P}}$ of $\mathcal{P}$ always be preserved?</p> http://mathoverflow.net/questions/126588/the-second-homology-of-a-group-g-and-presentation-complex-of-g The second homology of a group G and presentation complex of G Li Yu 2013-04-05T05:45:25Z 2013-04-05T08:19:03Z <p>Let $G$ be a finitely presentable group. If we assume $H_2(G,Z/pZ) =0$, $p$ is a prime, then can we always find a finite presentation $\mathcal{P}$ of $G$ so that its presentation complex $K_{\mathcal{P}}$ satisfies $H_2(K_{\mathcal{P}},Z/pZ)=0$?</p> http://mathoverflow.net/questions/110293/judging-whether-a-finitely-presented-group-is-a-3-manifold-group Judging whether a finitely presented group is a 3-manifold group? Li Yu 2012-10-22T02:38:39Z 2012-10-25T22:08:13Z <p>Given a finitely presented group $G$, how many necessary conditions do people know for $G$ to be isomorphic to the fundamental group of some closed connected 3-manifold? (e.g. residually finite)</p> http://mathoverflow.net/questions/109687/is-it-true-that-the-orbit-space-of-a-free-finite-group-action-on-a-cw-complex-is Is it true that the orbit space of a free finite group action on a CW-complex is also a CW-complex? Li Yu 2012-10-15T06:20:07Z 2012-10-15T21:45:19Z <p>Suppose a finite group G acts freely and continuously on an n-dimensional CW-complex X. Then can we conclude that the orbit space of this action is still an n-dimensional CW-complex? (or homotopy equivalent to an n-dimensional CW-complex?) In particular, we do not assume G acts cellularly on X.</p> http://mathoverflow.net/questions/126775/do-nielsen-transformations-on-a-presentation-preserve-the-homotopy-type-of-the-co/126806#126806 Comment by Li Yu Li Yu 2013-04-08T01:07:33Z 2013-04-08T01:07:33Z Thank you very much. This is exactly the reference I am looking for. http://mathoverflow.net/questions/126588/the-second-homology-of-a-group-g-and-presentation-complex-of-g Comment by Li Yu Li Yu 2013-04-05T13:48:20Z 2013-04-05T13:48:20Z HI: yeshengkui: $\pi_2(K_{\mathcal{P}})$ is not an invariant of $G$. So when we change the presentation $\mathcal{P}$ of $G$, the size of the second homotopy group of $K_{\mathcal{P}}$ may be reduced. http://mathoverflow.net/questions/125524/decomposition-of-solvable-lie-group/125575#125575 Comment by Li Yu Li Yu 2013-03-26T02:45:03Z 2013-03-26T02:45:03Z Thank you. But if G is linear, the answer to the question is Yes? http://mathoverflow.net/questions/110293/judging-whether-a-finitely-presented-group-is-a-3-manifold-group/110311#110311 Comment by Li Yu Li Yu 2012-10-22T10:09:40Z 2012-10-22T10:09:40Z Yes, that is what I'd like to know. http://mathoverflow.net/questions/110293/judging-whether-a-finitely-presented-group-is-a-3-manifold-group Comment by Li Yu Li Yu 2012-10-22T03:10:05Z 2012-10-22T03:10:05Z I know it is difficult to use them in practice. But I just want to know some such kind of conditions. http://mathoverflow.net/questions/109687/is-it-true-that-the-orbit-space-of-a-free-finite-group-action-on-a-cw-complex-is/109763#109763 Comment by Li Yu Li Yu 2012-10-16T02:48:24Z 2012-10-16T02:48:24Z I wonder when $G$ is finite and the CW-complex $X$ is of dimension $n$, can we choose the CW-complex homotopic to the orbit space $X/G$ to be $n$-dimensional too? http://mathoverflow.net/questions/109687/is-it-true-that-the-orbit-space-of-a-free-finite-group-action-on-a-cw-complex-is/109689#109689 Comment by Li Yu Li Yu 2012-10-15T13:56:22Z 2012-10-15T13:56:22Z I am very sorry. I thought the cellularly action case is easy. So I did not mention it at the beginning. But after your answer, I realize I should emphasize where the difficulty of the question lies. http://mathoverflow.net/questions/109687/is-it-true-that-the-orbit-space-of-a-free-finite-group-action-on-a-cw-complex-is/109689#109689 Comment by Li Yu Li Yu 2012-10-15T09:15:50Z 2012-10-15T09:15:50Z What I want to know is exactly the case when G does not acts cellularly!