DMCA
Academic adviser: Assessment committee: (2012)
BibTeX
@MISC{Homology12academicadviser:,
author = {Topological Hochschild Homology and Emanuele Dotto and Ib Madsen and Marcel Bökstedt and Bjørn Jan Dundas and C Emanuele Dotto},
title = {Academic adviser: Assessment committee:},
year = {2012}
}
Share
 |
 |
 |
 |
||
OpenURL
Abstract
The classical trace map is a highly non-trivial map from algebraic K-theory to topological Hochschild homology (or topological cyclic homology) introduced by Bökstedt, Hsiang and Madsen. It led to many computations of algebraic K-theory of rings. Hesselholt and Madsen recently introduced a Z/2-equivariant version of Waldhausen S�-construction for categories with duality. The output is a certain spectrum with involution, called the real K-theory spectrum, and associated bigraded groups KRp,q(C, D) analogous to Atiyah’s real (topological) K-groups. This thesis develops a theory of topological Hochschild homology for categories with duality, and a Z/2equivariant trace map from real K-theory to it. The main result of the thesis is the theorem that stable KR of the category of projective modules over a split square zero extension of a ring is equivalent to the real topological Hochschild homology of the ring with appropriate coefficients. This is the real version of the celebrated Dundas-McCarthy theorem for ordinary
Keyphrases
assessment committee academic adviser topological hochschild homology algebraic k-theory many computation main result 2-equivariant version waldhausen construction classical trace map stable kr real topological hochschild homology group krp projective module non-trivial map topological cyclic homology real version real k-theory spectrum trace map appropriate coefficient certain spectrum celebrated dundas-mccarthy theorem split square
