Volume 10 (2007)

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On the E¹–term of the gravity spectral sequence

Dai Tamaki

Geometry & Topology Monographs 10 (2007) 347–382

DOI: 10.2140/gtm.2007.10.347

arXiv: 0903.4704

Abstract

The author constructed a spectral sequence strongly converging to h*nΣn X) for any homology theory in [Topology 33 (1994) 631–662]. In this note, we prove that the E1-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 E1-term. Similar arguments can be also applied to its variants constructed in [Contemp Math 293 (2002) 299–329].

Keywords

Eilenberg–Moore spectral sequence, little cubes operad, cobar construction

Mathematical Subject Classification

Primary: 55T20

Secondary: 55P48

References
Publication

Received: 31 August 2004
Revised: 10 June 2005
Published: 18 April 2007

Authors
Dai Tamaki
Department of Mathematical Sciences
Shinshu University
Matsumoto 390-8621
Japan