User tweetie-bird - MathOverflow most recent 30 from http://mathoverflow.net 2013-05-26T02:42:57Z http://mathoverflow.net/feeds/user/23993 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/100555/jordan-curve-theorem-for-cylinders/100556#100556 Answer by tweetie-bird for Jordan curve theorem for cylinders tweetie-bird 2012-06-25T00:32:37Z 2012-06-25T00:57:49Z <p>This is the annulus theorem, and is indeed true for circles in $S^2$ without need for further hypotheses (which are needed in higher dimensions). </p> <p>See <a href="http://en.wikipedia.org/wiki/Annulus_theorem" rel="nofollow">en.wikipedia.org/wiki/Annulus_theorem</a></p> http://mathoverflow.net/questions/99506/blackbox-theorems/99526#99526 Answer by tweetie-bird for Blackbox Theorems tweetie-bird 2012-06-13T22:42:59Z 2012-06-14T02:23:39Z <p>How is the proof of the Poincare' Conjecture (in all dimensions) not yet anywhere on this list? </p> <p>Edit: in light of the comments below, this answer is now being upgraded to the proof of the Geometrization Conjecture (which implies the Poincare' Conjecture, among other things).</p> http://mathoverflow.net/questions/89692/if-graph-is-tree-what-can-be-said-about-its-adjacency-matrix/98981#98981 Answer by tweetie-bird for If graph is tree what can be said about its adjacency matrix ? tweetie-bird 2012-06-06T19:42:11Z 2012-06-06T23:52:59Z <p>A graph is bipartite iff the odd powers of the adjacency matrix have all 0's on the diagonal. So this implies that the sum of the $i$-th powers of the eigenvalues is 0 for each odd $i$. Since the adjacency matrix is symmetric, it has real eigenvalues. Thus, the eigenvalues are real numbers $\lambda_1,\dots ,\lambda_n$ with $\sum_{j=1}^n \lambda_j^i = 0$ for each odd $i$. </p> <p>I am guessing this probably should mean that the nonzero eigenvalues come in pairs of equal magnitude and opposite sign. I wonder if there is a good trick for efficiently proving this sort of thing -- about collections of real numbers satisfying such an infinite family of relations? (If so, I don't know this trick.)</p> <p>${\bf Edit:}$ Douglas Zare proved my above conjecture as a comment, so it is true for bipartite graphs that the nonzero eigenvalues of the adjacency matrix come in pairs of equal magnitude and opposite sign. </p> http://mathoverflow.net/questions/98821/how-often-do-people-read-the-work-that-they-cite/98828#98828 Answer by tweetie-bird for How often do people read the work that they cite? tweetie-bird 2012-06-05T00:17:24Z 2012-06-05T00:17:24Z <p>It depends whether I am citing the Poincare Conjecture or the five lemma. But I agree that either way, one should understand what one is doing well enough to use a result properly.</p> http://mathoverflow.net/questions/98082/etiquette-question-how-to-acknowledge-bugs-bunny Etiquette question: how to acknowledge Bugs Bunny? tweetie-bird 2012-05-27T02:55:05Z 2012-05-27T03:23:06Z <p>Suppose that a mathematician such as Bugs Bunny answers one of my math questions here on MathOverflow, and then I use the idea in a research paper. How should I acknowledge such a distinguished mathematician in my paper, submitted to a reputable journal and all that?</p> http://mathoverflow.net/questions/114245/i-know-that-you-know/114271#114271 Comment by tweetie-bird tweetie-bird 2012-11-24T11:59:11Z 2012-11-24T11:59:11Z I was really trying to understand this answer, but now need to get some other work done outside MathOverflow. http://mathoverflow.net/questions/114245/i-know-that-you-know/114271#114271 Comment by tweetie-bird tweetie-bird 2012-11-23T23:18:50Z 2012-11-23T23:18:50Z I deleted my previous comment so as not to confuse others. This logic puzzle is already confusing enough. http://mathoverflow.net/questions/112466/can-assumptions-about-forcing-produce-mice Comment by tweetie-bird tweetie-bird 2012-11-19T14:54:46Z 2012-11-19T14:54:46Z @Michael: it's not terribly clear from what you've written here what you are so upset about, but I'm sure everything will be fine if you just treat these mice fairly. I imagine these are grown-up mice you are talking about. http://mathoverflow.net/questions/112385/poincare-3-homology-sphere/112410#112410 Comment by tweetie-bird tweetie-bird 2012-11-17T14:20:22Z 2012-11-17T14:20:22Z Wouldn't Whitney embedding theorem need 6 dimensions? Am I missing something? Wikipedia says you start with an immersion with transverse self-intersections, then you fix this. (I paraphrase.) http://mathoverflow.net/questions/112385/poincare-3-homology-sphere Comment by tweetie-bird tweetie-bird 2012-11-14T21:15:05Z 2012-11-14T21:15:05Z I wonder if someone would add here the reference for the Freedman result. Thanks! http://mathoverflow.net/questions/111703/what-is-the-homotopy-type-of-the-space-of-the-homeomorphisms-of-the-n-ball-such-t Comment by tweetie-bird tweetie-bird 2012-11-10T00:59:29Z 2012-11-10T00:59:29Z I imagine in 6 you meant to say &quot;the restriction to the boundary is isotopic to the identity&quot;. Interesting question! http://mathoverflow.net/questions/110853/is-27-too-late-to-become-a-mathematician-or-something-else-that-is-math-intensive Comment by tweetie-bird tweetie-bird 2012-10-27T21:24:13Z 2012-10-27T21:24:13Z @GH: excellent summary of points already made recently on MO! http://mathoverflow.net/questions/60108/occurrences-of-cohomology-in-other-disciplines-and-or-nature/110622#110622 Comment by tweetie-bird tweetie-bird 2012-10-25T14:27:51Z 2012-10-25T14:27:51Z While this isn't so clear from the title of the question, the first sentence in the text of the question mentions wanting things outside of pure mathematics. http://mathoverflow.net/questions/110158/what-if-i-want-to-look-for-a-space-with-vanishing-first-homology-but-nonzero-fund/110203#110203 Comment by tweetie-bird tweetie-bird 2012-10-20T23:22:22Z 2012-10-20T23:22:22Z Thank you for your help. I was being dense. http://mathoverflow.net/questions/110158/what-if-i-want-to-look-for-a-space-with-vanishing-first-homology-but-nonzero-fund/110203#110203 Comment by tweetie-bird tweetie-bird 2012-10-20T22:48:34Z 2012-10-20T22:48:34Z I think the OP also wants the first homology group to be 0 -- going by the title of the question rather than the text. http://mathoverflow.net/questions/110052/enr-spaces-which-group-of-homeomorphisms-is-not-locally-contractable Comment by tweetie-bird tweetie-bird 2012-10-19T21:05:57Z 2012-10-19T21:05:57Z I wonder if you would be willing to explain a little more how these wild arcs work -- I don't like opening links on the web, and I'm having a little trouble understanding your question without reading the Siebenmann manuscript. Thanks! Anyway, perhaps you'll get more answers to your question if you explain the question a little more. http://mathoverflow.net/questions/57337/when-should-a-supervisor-be-a-co-author/109259#109259 Comment by tweetie-bird tweetie-bird 2012-10-10T00:58:10Z 2012-10-10T00:58:10Z What you've written is not an answer to the question. Meta is the place for this sort of meta-discussion. http://mathoverflow.net/questions/3559/colloquial-catchy-statements-encoding-serious-mathematics/3562#3562 Comment by tweetie-bird tweetie-bird 2012-10-10T00:42:23Z 2012-10-10T00:42:23Z Uh oh. Thanks for the warning. http://mathoverflow.net/questions/26821/is-thompsons-group-f-amenable/45891#45891 Comment by tweetie-bird tweetie-bird 2012-10-04T13:59:45Z 2012-10-04T13:59:45Z @Justin: good luck with your work on this difficult question! http://mathoverflow.net/questions/106230/schubert-varieties-which-admit-small-resolutions-of-singularities/106293#106293 Comment by tweetie-bird tweetie-bird 2012-09-04T02:12:12Z 2012-09-04T02:12:12Z That's interesting! In case you edit your answer again, I think MacPherson has a capital &quot;P&quot;.