 

Michael A. Hill and
Mingcong Zeng
Generalized Zhomotopy fixed points of C_{n} spectra with applications to norms of MU_{R}
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print


Published: 
January 11, 2020. 
Keywords: 
Equivariant homotopy, slice spectral sequence, homotopy fixed points. 
Subject: 
55Q91, 55P42, 55T99. 


Abstract
We introduce a computationally tractable way to describe the Zhomotopy fixed points of a C_{n}spectrum
E, producing a genuine C_{n} spectrum E^{hnZ} whose fixed and homotopy fixed points agree and are the
Zhomotopy fixed points of E. These form the bottom piece of a contravariant functor from the divisor poset of n to
genuine C_{n}spectra, and when E is an N_{∞}ring spectrum, this functor lifts to a functor
of N_{∞}ring spectra.
For spectra like the Real JohnsonWilson theories or the norms of Real bordism, the slice spectral sequence provides a way to easily compute the RO(G)graded homotopy groups of the spectrum E^{hnZ}, giving the homotopy groups of the
Zhomotopy fixed points. For the more general spectra in the contravariant functor, the slice spectral sequences interpolate between the one for the norm of Real bordism and the especially simple Zhomotopy fixed point case,
giving us a family of new tools to simplify slice computations. 

Acknowledgements
The first author was supported by NSF Grant DMS1811189.


Author information
Michael A. Hill:
Department of Mathematics
University of California at Los Angeles
Los Angeles, CA 90095, USA
mikehill@math.ucla.edu
Mingcong Zeng:
Department of Mathematics
Utrecht University
Utrecht, the Netherlands
m.zeng@uu.nl

