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2003 Arc operads and arc algebras
Ralph M Kaufmann, Muriel Livernet, R C Penner
Geom. Topol. 7(1): 511-568 (2003). DOI: 10.2140/gt.2003.7.511

Abstract

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.

Citation

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Ralph M Kaufmann. Muriel Livernet. R C Penner. "Arc operads and arc algebras." Geom. Topol. 7 (1) 511 - 568, 2003. https://doi.org/10.2140/gt.2003.7.511

Information

Received: 6 December 2002; Accepted: 8 June 2003; Published: 2003
First available in Project Euclid: 21 December 2017

zbMATH: 1034.18009
MathSciNet: MR2026541
Digital Object Identifier: 10.2140/gt.2003.7.511

Subjects:
Primary: 32G15
Secondary: 17Bxx, 18D50, 83E30

Rights: Copyright © 2003 Mathematical Sciences Publishers

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