2020/06/07 by Jonathan A. Campbell, J. Lind, Campbell, Jonathan A. +7
Mathematics · #16E40 #18D20 #55N15 #55P42 #Advanced Topics in Algebra #Algebraic Topology (math.AT) #Algebraic structures and combinatorial models #Category Theory (math.CT) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #K-Theory and Homology (math.KT)
paper · pdf · doi:10.48550/arxiv.2006.04006
openalex publication_date 2020/06/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We give an explicit point-set construction of the Dennis trace map from the K-theory of endomorphisms KEnd(C) to topological Hochschild homology THH(C) for any spectral Waldhausen category C. We describe the necessary technical foundations, most notably a well-behaved model for the spectral category of diagrams in C indexed by an ordinary category via the Moore end. This is applied to define a version of Waldhausen's S\bullet-construction for spectral Waldhausen categories, which is central to this account of the Dennis trace map. Our goals are both convenience and transparency---we provide all details except for a proof of the additivity theorem for THH, which is taken for granted---and the exposition is concerned not with originality of ideas, but rather aims to provide a useful resource for learning about the Dennis trace and its underlying machinery.