Title: Non-linear cyclic homology and the map to algebraic K-theory
Speaker: Crichton Ogle
Speaker Info: Ohio State
Brief Description:
Special Note:
Abstract:
Abstract: Building on methods that began with the speaker's 1984 thesis, and which incorporate the known connections between cyclic homology and (rational) algebraic K-theory proven since then, we will discuss the current status of Loday's conjecture (posed by J.L. Loday in 1982). In particular, we will detail the construction of a map from non-linear monomial cyclic homology into rational algebraic K-theory which extends the construction of Dennis-Stein symbols in K_2(R) for commutative rings R. We also give a conjectural description of the composition of this map with the Dennis trace map, and show how this is connected to the existence of two distinct cyclic structures on the non-linear Hochschild complex.Date: Thursday, March 12, 2020