This work introduced and characterized a class of polyloops called Moufang Polyloop and is devoted to studying some algebraic properties of this special class of polyloops. The Moufang identities in classical loop theory were adopted to conceptualize the Moufang polyloop. Moufang polyloop identities were characterized into Moufang polyloop-1, 2, 3 and 4. The flexibility law and some algebraic properties satisfied by each of these identities were studied.
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.
Note: Refreshments will be served 1:00 p.m. - 1:30 p.m. prior to the talk.
My collaboration with Jeff Fox: Mathematical and personal connections formed as products of Kasparov's bivariant K-theory
Dec. 03, 2024 3:30pm (MATH 3…
Topology
Alexander LaJeunesse
X
In this talk we will discuss the proof of the Land-Mathew-Meier-Tamme Purity Theorem in algebraic K-theory, and how the theorem implies half of the Chromatic Redshift conjecture.
Moufang Polyloop and its Algebraic Properties