On the spectral sequence of the Swiss-cheese operad

Hoefel, Eduardo¹ ; Livernet, Muriel²

¹Departamento de Matemática, Universidade Federal do Paraná, Universidade Federal do Paraná - C.P. 019081, 81531-990 Curitiba, PR - Brazil
²Sorbonne Paris Cité, Université Paris 13, LAGA, CNRS UMR 7539, 99 avenue Jean-Baptiste Clément, F-93430 Villetaneuse, France

Algebraic and Geometric Topology, Tome 13 (2013) no. 4, pp. 2039-2060

Résumé

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.

Détail

DOI : 10.2140/agt.2013.13.2039

Classification : 18G55, 18D50
Keywords: Koszul Operads, Homotopy Algebras, Deformation Theory

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