Celebratio Mathematica — Baum

Twisted K-homology and Paul Baum

Works connected to Ronald George Douglas

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P. Baum and R. G. Douglas: “Index theory, bordism, and \( K \)-homology,” pp. 1–31 in Operator algebras and \( K \)-theory (San Francisco, 7–8 January 1981). Edited by R. G. Douglas and C. Schochet. Contemporary Mathematics 10. American Mathematical Society (Providence, RI), 1982. MR 658506 Zbl 0507.55004 incollection

Our purpose in this note is threefold. After giving brief and selective descriptions of the topological and analytical realizations of \( K \)-homology, we present our view of index theory. Sedond, we shall say more about our proof of the isomorphism of topological and analytical realizations of \( K \)-homology since that lies at the heart of matters. In particular, we want to discuss the bordism step of the proof since this makes contact with a number of interesting topics including relative \( K \)-homology and elliptic boundary value problems. Lastly, we want to work out a key step in the bordism proof in two special cases where the result may have independent interest.

Claude L. Schochet	Related
Ronald George Douglas	Related

P. Baum and R. G. Douglas: “\( K \) homology and index theory,” pp. 117–173 in Operator algebras and applications (Kingston, ON, 14 July–2 August 1980), part 1. Edited by R. V. Kadison. Proceedings of Symposia in Pure Mathematics 38. American Mathematical Society (Providence, RI), 1982. MR 679698 Zbl 0532.55004 incollection

Ronald George Douglas	Related
Richard V. Kadison	Related