Jeff Fox and I met in 1983. We were intrigued by Kasparov's elegant and powerful bivariant K-theory, and we dared hope it would allow us to use Jeff's background in representation theory and mine in topology to prove cases of the Baum-Connes and Connes-Kasparov conjectures. The depth of the challenges posed by those conjectures was greater than we first imagined, but, largely due to Jeff's knowledge of representation theory, we did make a contribution to the area. We also proved some representation-multiplicity index theorems for transversally elliptic operators. These results illustrated K-theory's ability to extract representation-theoretic integer-valued invariants from group C*-algebras. Other work we did involved index theory for singular spaces, pushing inspiration from Riemann-Roch theorems in directions that involved enough analysis to suggest roles for spectral invariants. I learned much mathematics and much about how to do mathematics from Jeff. Working with him, I got to know one of the kindest, most generous people I have ever met.
My collaboration with Jeff Fox: Mathematical and personal connections formed as products of Kasparov's bivariant K-theory
My collaboration with Jeff Fox: Mathematical and personal connections formed as products of Kasparov's bivariant K-theory