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Mathematische Annalen

, Volume 317, Issue 3, pp 613–628 | Cite as

Higher genus surface operad detects infinite loop spaces

  • Ulrike Tillmann
Original article

Abstract. The operad studied in conformal field theory and introduced ten years ago by G. Segal [S] is built out of moduli spaces of Riemann surfaces. We show here that this operad which at first sight is a double loop space operad is indeed an infinite loop space operad. This leads to a new proof of the fact that the classifying space of the stable mapping class group \(\mathbb Z \times B\Gamma_\infty ^+\), is an infinite loop space after plus construction [T2]. This new approach has various advantages. In particular, the infinite loop space structure is more explicid.

Mathematics Subject Classification (1991): 55P47, 32G15, 81T40, 55R35 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2000

Authors and Affiliations

  • Ulrike Tillmann
    • 1
  1. 1.Mathematical Institute, 24-29 St. Giles Street, Oxford OX1 3LB, UK (e-mail: tillmann@maths.ox.ac.uk) GB

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