Comments on: Torsion in the homology of 3-manifolds http://blogs.ethz.ch/kowalski/2009/06/23/torsion-in-the-homology-of-3-manifolds/ Comments on mathematics, mostly. Wed, 25 Jan 2012 12:23:22 +0000 hourly 1 http://wordpress.org/?v=3.3.1 By: Math World | E. Kowalski's blog › Torsion in the homology of 3-manifolds http://blogs.ethz.ch/kowalski/2009/06/23/torsion-in-the-homology-of-3-manifolds/#comment-14174 Math World | E. Kowalski's blog › Torsion in the homology of 3-manifolds Fri, 14 Aug 2009 20:00:12 +0000 http://blogs.ethz.ch/kowalski/?p=1066#comment-14174 [...] View post:  E. Kowalski's blog › Torsion in the homology of 3-manifolds [...] [...] View post:  E. Kowalski's blog › Torsion in the homology of 3-manifolds [...]

]]> By: Kowalski http://blogs.ethz.ch/kowalski/2009/06/23/torsion-in-the-homology-of-3-manifolds/#comment-12497 Kowalski Wed, 24 Jun 2009 05:14:14 +0000 http://blogs.ethz.ch/kowalski/?p=1066#comment-12497 Indeed, Akshay mentioned the two collaborations (and their respective content); he discussed the connection with Galois representations at the end of his talk. That's quite fascinating also... The need of initialing the names of two of the people involved in these stories to avoid confusion is amusing. (And thanks for the correction about the quadratic field). Indeed, Akshay mentioned the two collaborations (and their respective content); he discussed the connection with Galois representations at the end of his talk. That’s quite fascinating also…

The need of initialing the names of two of the people involved in these stories to avoid confusion is amusing.

(And thanks for the correction about the quadratic field).

]]> By: Anonymous http://blogs.ethz.ch/kowalski/2009/06/23/torsion-in-the-homology-of-3-manifolds/#comment-12495 Anonymous Wed, 24 Jun 2009 04:02:39 +0000 http://blogs.ethz.ch/kowalski/?p=1066#comment-12495 I'm not sure exactly what Akshay talked about, but I should clarify that there are two collaborations, one between Venkatesh and Bergeron, and one between Venkatesh and Calegari. The concern of the latter paper is the (conjectural) connection between these torsion classes and Galois representations. The field in the example you alluded to is Q(sqrt(-2)). The isometry group of H_3 is (essentially) PGL_2(C), and PGL_2(Z_K) is a discrete finite co-volume subgroup of PGL_2(C) exactly when [K:Q] = 2 and K is imaginary. These examples were produced by Dunfield during the writing of F.Calegari-Dunfield^* in an effort to test a possible generalization of the Jacquet-Langlands correspondence for GL(2)to torsion classes. (Such a generalization appears to be true, and is one of the main concerns of Calegari-Venkatesh). *not to be confused with D.Calegari-Dunfield. On that note, you could also have written Dunfield-W.Thurston to distinguish it from Dunfield-D.Thurston. I’m not sure exactly what Akshay talked about, but I should clarify that there are two collaborations, one between Venkatesh and Bergeron, and one between Venkatesh and Calegari. The concern of the latter paper is the (conjectural) connection between these torsion classes and Galois representations.

The field in the example you alluded to is Q(sqrt(-2)). The isometry group of H_3 is (essentially) PGL_2(C), and PGL_2(Z_K) is a discrete finite co-volume subgroup of PGL_2(C) exactly when [K:Q] = 2 and K is imaginary. These examples were produced by Dunfield during the writing of F.Calegari-Dunfield^* in an effort to test a possible generalization of the Jacquet-Langlands correspondence for GL(2)to torsion classes. (Such a generalization appears to be true, and is one of the main concerns of Calegari-Venkatesh).

*not to be confused with D.Calegari-Dunfield. On that note, you could also have written Dunfield-W.Thurston to distinguish it from Dunfield-D.Thurston.

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