User luis jorge - MathOverflow most recent 30 from http://mathoverflow.net 2013-05-20T20:23:28Z http://mathoverflow.net/feeds/user/19318 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/98432/torsion-of-bass-farrell-and-waldhausen-nil-groups Torsion of Bass, Farrell and Waldhausen nil groups Luis Jorge 2012-05-30T22:45:49Z 2012-05-30T22:45:49Z <p>Let H be an infinite virtually cyclic group. If H is orientable (resp. non-orientable) the Farrell nil groups $N_n(\mathbb{Z}H,\alpha)$ (resp. the Waldhausen nil groups $N^W_n(\mathbb{Z}H;\mathbb{Z}[G_1-H],\mathbb{Z}[G_1-H])$), are torsion groups?</p> http://mathoverflow.net/questions/95082/k-theory-of-mathbbz k-theory of $\mathbb{Z}$ Luis Jorge 2012-04-24T22:19:34Z 2012-04-24T22:19:34Z <p>I have a doubt.</p> <p>Borel computed the rank of the higher algebraic k-theory of $\mathbb{Z}$:</p> <p>$rank(K_n)(\mathbb{Z})= 1$ if $n\equiv1 mod4$, otherwise this rank is equal to 0.</p> <p>On the other hand Bjorn Jahren proved for any finite group $G$ that </p> <p>$rank(K_n(\mathbb{Z}[G]))=c$ if $n\equiv3 mod4$, where c is the number of irreductible complex representation of G.</p> <p>If I let $G=1$, then I have that $rank(K_n)(\mathbb{Z})= 1$ if $n\equiv3 mod4$...</p> <p>this is a contradiction with Borel's result. What happened here? Am I wrong? (I hope so)</p> http://mathoverflow.net/questions/89217/the-k-theoretic-farrell-jones-conjecture-for-cat0-groups The K-theoretic Farrell-Jones conjecture for cat(0) groups Luis Jorge 2012-02-22T18:20:46Z 2012-02-22T20:52:15Z <p>Is the fibered K-theoretic farrell-jones conjecture true for cat(0)-groups?</p> http://mathoverflow.net/questions/83127/examples-of-cat0-groups Examples of CAT(0)-groups Luis Jorge 2011-12-10T16:13:27Z 2011-12-10T16:16:32Z <p>My question is the following:</p> <p>Let M be a simply connected Riemannian manifold whose sectional curvatures are all nonpositive and let G be a group. Suppose that G acts in M properly discontinuous and cocompactly by isometries. Is G a CAT(0) group?</p> http://mathoverflow.net/questions/81841/closed-surfaces-are-aspherical Closed surfaces are aspherical? Luis Jorge 2011-11-24T23:50:58Z 2011-11-24T23:58:28Z <p>Let M be a closed surface with non empty boundary. Is M Aspherical? Let $C\subset M$ be a finite subset. Is M-C aspherical?</p> http://mathoverflow.net/questions/81112/hyperbolicity-of-a-semidirect-product Hyperbolicity of a semidirect product Luis Jorge 2011-11-16T20:09:19Z 2011-11-16T20:15:11Z <p>Let F be a finitely generated free group and let $\gamma : F \rightarrow F$ be an automorphism. Is the semidirect product $F \rtimes \mathbb{Z}$ an hyperbolic group? where $\mathbb{Z}$ acts in F via $\gamma$.</p> http://mathoverflow.net/questions/95082/k-theory-of-mathbbz Comment by Luis Jorge Luis Jorge 2012-04-24T22:41:39Z 2012-04-24T22:41:39Z A very naive mistake I think. Thank you http://mathoverflow.net/questions/89217/the-k-theoretic-farrell-jones-conjecture-for-cat0-groups/89221#89221 Comment by Luis Jorge Luis Jorge 2012-02-22T20:46:56Z 2012-02-22T20:46:56Z Thank you very much for your answer. http://mathoverflow.net/questions/89217/the-k-theoretic-farrell-jones-conjecture-for-cat0-groups/89221#89221 Comment by Luis Jorge Luis Jorge 2012-02-22T18:51:30Z 2012-02-22T18:51:30Z But also they proved the fibered version? http://mathoverflow.net/questions/81841/closed-surfaces-are-aspherical Comment by Luis Jorge Luis Jorge 2011-11-25T00:09:52Z 2011-11-25T00:09:52Z Thank you very much, in fact, I have mistakes in my redaction but your answers are very useful for me. http://mathoverflow.net/questions/81112/hyperbolicity-of-a-semidirect-product/81113#81113 Comment by Luis Jorge Luis Jorge 2011-11-17T19:47:09Z 2011-11-17T19:47:09Z I have one more question, If $\gamma$ is induced by a diffeomorphism $f: M\rightarrow M$ where M is a compact 2 manifold with boundary and $\pi_1 (M)$ is isomorphic to F, then my initial demidirect product is hyperbolic? http://mathoverflow.net/questions/81112/hyperbolicity-of-a-semidirect-product/81113#81113 Comment by Luis Jorge Luis Jorge 2011-11-16T20:27:53Z 2011-11-16T20:27:53Z Is this semidirect product a CAT(0) group?