User tye lidman - MathOverflow most recent 30 from http://mathoverflow.net 2013-05-19T23:18:57Z http://mathoverflow.net/feeds/user/3405 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/97432/when-is-a-three-manifold-deck-transformation-group-solvable When is a three-manifold deck transformation group solvable? Tye Lidman 2012-05-19T20:56:20Z 2012-05-19T23:09:36Z <p>Suppose that $\pi:Y \to Y'$ is a regular covering of closed, connected, orientable three-manifolds and let $G$ be the deck transformation group. Furthermore, suppose that $Y$ is a rational homology sphere (I don't know how much this condition matters). It's not always the case that $G$ is solvable, since one can take $Y$ to be $S^3$ and $Y'$ to be the Poincare homology sphere. Are there other examples where $G$ is not solvable? Are such examples classified? If $Y$ has elliptic geometry, this is the only example (I think), but I have no clue in general. This seems like it could be related to residual finiteness of three-manifold groups/RFRS/LERF/other four-letter acronyms I don't understand.</p> http://mathoverflow.net/questions/94724/how-to-compute-the-monopole-floer-homology-for-surface-times-s1/95580#95580 Answer by Tye Lidman for How to compute the Monopole Floer Homology for Surface $\times S^1$ ? Tye Lidman 2012-04-30T15:02:58Z 2012-04-30T15:02:58Z <p>I would assume you are interested in $HM$-to as opposed to $HM$-bar ($HM$-bar is mostly computed in the book Monopoles and 3-manifolds by Kronheimer and Mrowka). For the case of $HM$-to, you should use (as answered above) that monopole is isomorphic to Heegaard Floer (Kutluhan-Lee-Taubes or Taubes + Colin-Ghiggini-Honda). </p> <p>If you want the trivial torsion Spin$^c$ structure, this is computed by Jabuka and Mark: <a href="http://arxiv.org/pdf/math/0502328v4.pdf" rel="nofollow">http://arxiv.org/pdf/math/0502328v4.pdf</a></p> <p>This paper also has the references to the earlier computations for the other Spin$^c$ structures, done by Ozsvath and Szabo.</p> http://mathoverflow.net/questions/10671/relating-euler-characteristic-intersection-product-morse-theory-plus-su2-and/12379#12379 Answer by Tye Lidman for Relating Euler characteristic, intersection product, Morse theory (plus SU(2) and 3-manifolds) Tye Lidman 2010-01-20T05:34:51Z 2010-01-20T05:34:51Z <p>It might be helpful to look at the book of Akbulut and McCarthy on Casson's Invariant. I think the answer to Question 1 is fairly clearly explained in Proposition 1.1b of of Chapter III. </p> http://mathoverflow.net/questions/97432/when-is-a-three-manifold-deck-transformation-group-solvable/97438#97438 Comment by Tye Lidman Tye Lidman 2012-05-19T22:05:46Z 2012-05-19T22:05:46Z Yes, that is a good observation. I really want to restrict to rational homology spheres then.