On the E^1-term of the gravity spectral sequence

Details On the E^1-term of the gravity spectral sequence On the E^1-term of the gravity spectral sequence

2009-03-26

arxiv.org/abs/0903.4704v1

Geom. Topol. Monogr. 10 (2007) 347-382

Mathematics

Algebraic Topology

This is the version published by Geometry & Topology Monographs on 18 April 2007

Scientific paper

10.2140/gtm.2007.10.347

The author constructed a spectral sequence strongly converging to h_*(Omega^n Sigma^n X) for any homology theory in [Topology 33 (1994) 631-662]. In this note, we prove that the E^1-term of the spectral sequence is isomorphic to the cobar construction, and hence the spectral sequence is isomorphic to the classical cobar-type Eilenberg-Moore spectral sequence based on the geometric cobar construction from the E^1-term. Similar arguments can be also applied to its variants constructed in [Contemp Math 293 (2002) 299-329].

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