Topological Hochschild Homology of $K/p$ as a $K_p^\wedge$ module

Details Topological Hochschild Homology of $K/p$ as a $K_p^\wedge$ module Topological Hochschild Homology of $K/p$ as a $K_p^\wedge$ module

2010-06-22

arxiv.org/abs/1006.4347v2

Mathematics

Algebraic Topology

Scientific paper

Let $R$ be an $E_\infty$-ring spectrum. Given a map $\zeta$ from a space $X$ to $BGL_1R$, one can construct a Thom spectrum, $X^\zeta$, which generalises the classical notion of Thom spectrum for spherical fibrations in the case $R=S^0$, the sphere spectrum. If $X$ is a loop space ($\simeq \Omega Y$) and $\zeta$ is homotopy equivalent to $\Omega f$ for a map $f$ from $Y$ to $B^2GL_1R$, then the Thom spectrum has an $A_\infty$-ring structure. The Topological Hochschild Homology of these $A_\infty$-ring spectra is equivalent to the Thom spectrum of a map out of the free loop space of $Y$. This paper considers the case $X=S^1$, $R=K_p^\wedge$, the p-adic $K$-theory spectrum, and $\zeta = 1-p \in \pi_1BGL_1K_p^\wedge$. The associated Thom spectrum $(S^1)^\zeta$ is equivalent to the mod p $K$-theory spectrum $K/p$. The map $\zeta$ is homotopy equivalent to a loop map, so the Thom spectrum has an $A_\infty$-ring structure. I will compute $\pi_*THH^{K_p^\wedge}(K/p)$ using its description as a Thom spectrum.

Affiliated with

Also associated with

No associations

Rating

Topological Hochschild Homology of $K/p$ as a $K_p^\wedge$ module does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Topological Hochschild Homology of $K/p$ as a $K_p^\wedge$ module, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Topological Hochschild Homology of $K/p$ as a $K_p^\wedge$ module will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-108685