User alexander thumm - MathOverflow most recent 30 from http://mathoverflow.net 2013-05-18T12:02:13Z http://mathoverflow.net/feeds/user/11040 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/69117/cohomological-dimension-of-mathcalb-n/74831#74831 Answer by Alexander Thumm for Cohomological dimension of $\mathcal{B}_n$ Alexander Thumm 2011-09-08T06:18:43Z 2011-09-08T06:18:43Z <p>I will sadly have to answer to this old post to elaborate on the lower bound part of Agol's answer. I would be grateful if someone could turn this into a comment.</p> <p>It is in fact quite easy to find a subgroup of $P_n$ isomorphic to $\mathbb Z^{n-1}$. It is generated by the full twist of the first $k$ strands, where $k= 2,3,\dots, n$.</p> http://mathoverflow.net/questions/56908/two-nonequivalent-complete-norms-on-the-same-space two nonequivalent complete norms on the same space Alexander Thumm 2011-02-28T16:23:14Z 2011-02-28T16:36:45Z <p>I recently stumbled upon following reasoning:</p> <p>"Let $X$ be a banachspace with respect to the norms $|\cdot |_1$ and $|\cdot |_2$. Define $|x | := |x |_1 + |x |_2$. Clearly $id: (X,|\cdot|) \to (X,|\cdot|_i)$ is continuous and invertible. Since $(X,|\cdot|)$ is also a banachspace, all three norms must be equivalent by the open mapping theorem."</p> <p>The problem is, I do not see any reason, why $(X,|\cdot|)$ should be a banachspace but I am unable to construct a counterexample and I think such a counterexample would be rather unintuitive.</p> <p>I would like to know, wheter or not the above statement is true. If not, is there an easy counterexample?</p> http://mathoverflow.net/questions/52952/weak-regularity-conditions-for-regions-to-assure-boundary-of-measure-zero weak regularity conditions for regions to assure boundary of measure zero Alexander Thumm 2011-01-23T13:39:43Z 2011-01-23T13:39:43Z <p>Let $\Omega \subset \mathbb{R}^d$ be a region ( bounded, simply connected, open set ). What are some regularity conditions to assure the boundary $\partial\Omega$ is a set of (lebesgue-)measure zero? Is there any geometric / topological condition, which is equivalent to the statement that $\mu(\partial\Omega) = 0$?</p> <p>I am particularly interested in some weak conditions, in a sense of not being too restrictive. I'm not interested in statements as strong as "if $\partial\Omega$ is a submanifold, ...".</p> http://mathoverflow.net/questions/52952/weak-regularity-conditions-for-regions-to-assure-boundary-of-measure-zero Comment by Alexander Thumm Alexander Thumm 2011-01-24T09:02:49Z 2011-01-24T09:02:49Z As this condition seems very natural to protect onesself from spacefillung boundaries, I do not see that it makes any use of $\Omega$ being a region. On the other hand I do not now how to use this information without stating very strong requirements. http://mathoverflow.net/questions/21003/polynomial-bijection-from-qxq-to-q/47137#47137 Comment by Alexander Thumm Alexander Thumm 2010-11-23T19:30:10Z 2010-11-23T19:30:10Z Ok, i just recognized my error of thought there...