Volume 14, issue 6 (2014)

Download this article
Download this article For screen
For printing
Recent Issues

Volume 24
Issue 2, 595–1223
Issue 1, 1–594

Volume 23, 9 issues

Volume 22, 8 issues

Volume 21, 7 issues

Volume 20, 7 issues

Volume 19, 7 issues

Volume 18, 7 issues

Volume 17, 6 issues

Volume 16, 6 issues

Volume 15, 6 issues

Volume 14, 6 issues

Volume 13, 6 issues

Volume 12, 4 issues

Volume 11, 5 issues

Volume 10, 4 issues

Volume 9, 4 issues

Volume 8, 4 issues

Volume 7, 4 issues

Volume 6, 5 issues

Volume 5, 4 issues

Volume 4, 2 issues

Volume 3, 2 issues

Volume 2, 2 issues

Volume 1, 2 issues

The Journal
About the Journal
Editorial Board
Editorial Interests
Submission Guidelines
Submission Page
Policies for Authors
Ethics Statement
ISSN (electronic): 1472-2739
ISSN (print): 1472-2747
Author Index
To Appear
Other MSP Journals
The $T$–algebra spectral sequence: Comparisons and applications

Justin Noel

Algebraic & Geometric Topology 14 (2014) 3395–3417

In previous work with Niles Johnson the author constructed a spectral sequence for computing homotopy groups of spaces of maps between structured objects such as G–spaces and n–ring spectra. In this paper we study special cases of this spectral sequence in detail. Under certain assumptions, we show that the Goerss–Hopkins spectral sequence and the T–algebra spectral sequence agree. Under further assumptions, we can apply a variation of an argument due to Jennifer French and show that these spectral sequences agree with the unstable Adams spectral sequence.

From these equivalences we obtain information about the filtration and differentials. Using these equivalences we construct the homological and cohomological Bockstein spectral sequences topologically. We apply these spectral sequences to show that Hirzebruch genera can be lifted to –ring maps and that the forgetful functor from –algebras in HF ̄p–modules to H–algebras is neither full nor faithful.

spectral sequence, orientations, structured ring spectra, power operations, rational homotopy theory, unstable homotopy theory
Mathematical Subject Classification 2010
Primary: 55P99, 55S35
Secondary: 13D03, 18C15
Received: 27 August 2013
Revised: 25 March 2014
Accepted: 8 April 2014
Published: 15 January 2015
Justin Noel
University of Regensburg
NWF I - Mathematik
Universitätsstr. 31
93040 Regensburg