Geometry & Topology
- Geom. Topol.
- Volume 22, Number 2 (2018), 693-756.
Detecting periodic elements in higher topological Hochschild homology
Given a commutative ring spectrum , let be the Loday functor constructed by Brun, Carlson and Dundas. Given a prime , we calculate and for , and use these results to deduce that in the connective Morava K-theory of is nonzero and detected in the homotopy fixed-point spectral sequence by an explicit element, whose class we name the Rognes class.
To facilitate these calculations, we introduce multifold Hopf algebras. Each axis circle in gives rise to a Hopf algebra structure on , and the way these Hopf algebra structures interact is encoded with a multifold Hopf algebra structure. This structure puts several restrictions on the possible algebra structures on and is a vital tool in the calculations above.
Geom. Topol., Volume 22, Number 2 (2018), 693-756.
Received: 6 March 2014
Revised: 2 May 2017
Accepted: 4 June 2017
First available in Project Euclid: 1 February 2018
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Veen, Torleif. Detecting periodic elements in higher topological Hochschild homology. Geom. Topol. 22 (2018), no. 2, 693--756. doi:10.2140/gt.2018.22.693. https://projecteuclid.org/euclid.gt/1517454107