Higher genus surface operad detects infinite loop spaces

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 , 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. Received: 21 September 1998 / Revised: 30 August 1999 / Published online: 8 May 2000