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2018 Detecting periodic elements in higher topological Hochschild homology
Torleif Veen
Geom. Topol. 22(2): 693-756 (2018). DOI: 10.2140/gt.2018.22.693

Abstract

Given a commutative ring spectrum R, let ΛXR be the Loday functor constructed by Brun, Carlson and Dundas. Given a prime p5, we calculate π(ΛSnHFp) and π(ΛTnHFp) for np, and use these results to deduce that vn1 in the (n1)st connective Morava K-theory of (ΛTnHFp)hTn 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 Tn gives rise to a Hopf algebra structure on π(ΛTnHFp), 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 π(ΛTnHFp) and is a vital tool in the calculations above.

Citation

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Torleif Veen. "Detecting periodic elements in higher topological Hochschild homology." Geom. Topol. 22 (2) 693 - 756, 2018. https://doi.org/10.2140/gt.2018.22.693

Information

Received: 6 March 2014; Revised: 2 May 2017; Accepted: 4 June 2017; Published: 2018
First available in Project Euclid: 1 February 2018

zbMATH: 1384.55007
MathSciNet: MR3748678
Digital Object Identifier: 10.2140/gt.2018.22.693

Subjects:
Primary: 55P42, 55P91, 55T99

Rights: Copyright © 2018 Mathematical Sciences Publishers

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Vol.22 • No. 2 • 2018
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