TY - BOOK

T1 - Real Topological Cyclic Homology

AU - Høgenhaven, Amalie

PY - 2016

Y1 - 2016

N2 - The main topics of this thesis are real topological Hochschild homology and real topological cyclic homology. If a ring or a ring spectrum is equipped with an anti-involution, then it induces additional structure on the topological Hochschild homology spectrum. The group O(2) acts on the spectrum, where O(2) is the semi-direct product of T, the multiplicative group of complex number of modulus 1, by the group G=Gal(C/R). We refer to this O(2)-spectrum as the real topological Hochschild homology. This generalization leads to a G-equivariant version of topological cyclic homology, which we call real topological cyclic homology.The first part of the thesis computes the G-equivariant homotopy type of the real topological cyclic homology of spherical group rings at a prime p with anti-involution induced by taking inverses in the group. The second part of the thesis investigates the derived G-geometric fixed points of the real topological Hochschild homology of an ordinary ring with an anti-involution.

AB - The main topics of this thesis are real topological Hochschild homology and real topological cyclic homology. If a ring or a ring spectrum is equipped with an anti-involution, then it induces additional structure on the topological Hochschild homology spectrum. The group O(2) acts on the spectrum, where O(2) is the semi-direct product of T, the multiplicative group of complex number of modulus 1, by the group G=Gal(C/R). We refer to this O(2)-spectrum as the real topological Hochschild homology. This generalization leads to a G-equivariant version of topological cyclic homology, which we call real topological cyclic homology.The first part of the thesis computes the G-equivariant homotopy type of the real topological cyclic homology of spherical group rings at a prime p with anti-involution induced by taking inverses in the group. The second part of the thesis investigates the derived G-geometric fixed points of the real topological Hochschild homology of an ordinary ring with an anti-involution.

UR - https://soeg.kb.dk/permalink/45KBDK_KGL/fbp0ps/alma99122937685305763

M3 - Ph.D. thesis

BT - Real Topological Cyclic Homology

PB - Department of Mathematical Sciences, Faculty of Science, University of Copenhagen

ER -