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G&T Monographs |
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Arc operads and arc algebras
Ralph M Kaufmann, Muriel Livernet and R C Penner
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Geometry & Topology 7 (2003)
511–568
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Abstract
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Several topological and homological operads based on families of projectively
weighted arcs in bounded surfaces are introduced and studied. The spaces underlying
the basic operad are identified with open subsets of a combinatorial compactification
due to Penner of a space closely related to Riemann’s moduli space. Algebras
over these operads are shown to be Batalin–Vilkovisky algebras, where the
entire BV structure is realized simplicially. Furthermore, our basic operad
contains the cacti operad up to homotopy. New operad structures on the circle
are classified and combined with the basic operad to produce geometrically
natural extensions of the algebraic structure of BV algebras, which are also
computed.
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Keywords
moduli of Surfaces, operads,
Batalin–Vilkovisky algebras
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Mathematical Subject Classification
Primary: 32G15
Secondary: 17BXX, 18D50, 83E30
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Publication
Received: 6 December 2002
Accepted: 8 June 2003
Published: 18 August 2003
Proposed: Shigeyuki Morita
Seconded: Ralph Cohen, Vaughan Jones
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