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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
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