On the slice spectral sequence

Ullman, John

doi:10.2140/agt.2013.13.1743

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On the slice spectral sequence

John Ullman

Algebraic & Geometric Topology 13 (2013) 1743–1755

DOI: 10.2140/agt.2013.13.1743

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/

Volume 13, issue 3 (2013)