Volume 13, issue 3 (2013)

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ISSN (electronic): 1472-2739
ISSN (print): 1472-2747
On the slice spectral sequence

John Ullman

Algebraic & Geometric Topology 13 (2013) 1743–1755
Abstract

We introduce a variant of the slice spectral sequence which uses only regular slice cells, and state the precise relationship between the two spectral sequences. We analyze how the slice filtration of an equivariant spectrum that is concentrated over a normal subgroup is related to the slice filtration of its geometric fixed points, and use this to prove a conjecture of Hill on the slice filtration of an Eilenberg-MacLane spectrum (arXiv:1107.3582v1). We also show how the (co)connectivity of a spectrum results in the (co)connectivity of its slice tower, demonstrating the “efficiency” of the slice spectral sequence.

Keywords
slice, spectral sequence, equivariant, stable homotopy groups
Mathematical Subject Classification 2010
Primary: 55T99, 55N91, 55P91
Secondary: 55Q91
References
Publication
Received: 12 June 2012
Revised: 29 October 2012
Accepted: 12 November 2012
Published: 18 May 2013
Authors
John Ullman
Department of Mathematics
Massachusetts Institute of Technology
77 Massachusetts Avenue
Cambridge, MA 02139
USA
http://math.mit.edu/~jrullman/