Celebratio Mathematica — Baum — Complete Bibliography

Complete Bibliography

Works connected to Peter Robert Kotiuga

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P. Baum: “Dirac operator and \( K \)-theory for discrete groups,” pp. 97–107 in A celebration of the mathematical legacy of Raoul Bott (Montreal, 9–13 June 2008). Edited by P. R. Kotiuga. CRM Proceedings & Lecture Notes 50. American Mathematical Society (Providence, RI), 2010. MR 2648889 Zbl 1201.19001 incollection

Let \( G \) be a locally compact, Hausdorff, and second countable (i.e. the topology has a countable base) topological group. Examples are Lie groups, \( p \)-adic groups, adelic groups, and discrete groups. In 1980, P. Baum and A. Connes proposed an answer to the problem of calculating the \( K \)-theory of the reduced \( C^* \) algebra of \( G \). When true, the conjecture has several corollaries. Among these are exhaustion of the discrete series by Dirac induction, Novikov conjecture on homotopy invariance of higher signatures, amd Gromov–Lawson–Rosenberg conjecture on Riemannian metrics of positive scalar curvature. Since 1980, the conjecture has been proved for many examples. Although it seems quite possible that eventually there will be a discrete group which is a counter-example, at the present moment there is no really good candidate for a counter-example. This talk will explain the conjecture, concentrating on the case of discrete groups from the point of view of the index of elliptic operators. The talk is intended for non-specialists. All the basic definitions (\( C^* \) algebra, \( K \)-theory etc) will be carefully stated.

Raoul H. Bott	Related	Volume
Peter Robert Kotiuga	Related