Arc operads and arc algebras

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.

Keywords

moduli of Surfaces, operads, Batalin–Vilkovisky algebras

Mathematical Subject Classification 2000

Primary: 32G15

Secondary: 18D50, 17BXX, 83E30

References

Forward citations

Publication

Received: 6 December 2002

Accepted: 8 June 2003

Published: 18 August 2003

Proposed: Shigeyuki Morita

Seconded: Ralph Cohen, Vaughan Jones

Authors

Ralph M Kaufmann
Oklahoma State University Stillwater USA	Max Planck Institut für Mathematik Bonn Germany

Muriel Livernet
Université Paris 13 France

R C Penner
University of Southern California Los Angeles USA

Volume 7, issue 1 (2003)

Ralph M Kaufmann, Muriel Livernet and R C Penner