On the spectral sequence of the Swiss-cheese operad

Hoefel, Eduardo; Livernet, Muriel

doi:10.2140/agt.2013.13.2039

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On the spectral sequence of the Swiss-cheese operad

Eduardo Hoefel and Muriel Livernet

Algebraic & Geometric Topology 13 (2013) 2039–2060

DOI: 10.2140/agt.2013.13.2039

Abstract

We prove that the homology of the Swiss-cheese operad is a Koszul operad. As a consequence, we obtain that the spectral sequence associated to the stratification of the compactification of points on the upper half plane collapses at the second stage, proving a conjecture by A Voronov [Contemp. Math. 239 (1999) 365–373]. However, we prove that the operad obtained at the second stage differs from the homology of the Swiss-cheese operad.

Keywords

Koszul Operads, Homotopy Algebras, Deformation Theory

Mathematical Subject Classification 2010

Primary: 18G55, 18D50

References

Publication

Received: 17 October 2012

Revised: 1 February 2013

Accepted: 1 February 2013

Published: 29 May 2013

Authors

Eduardo Hoefel
Departamento de Matemática Universidade Federal do Paraná Universidade Federal do Paraná - C.P. 019081 81531-990 Curitiba, PR - Brazil

Muriel Livernet
Sorbonne Paris Cité Université Paris 13 LAGA, CNRS UMR 7539, 99 avenue Jean-Baptiste Clément F-93430 Villetaneuse, France

Volume 13, issue 4 (2013)