Higher genus surface operad detects infinite loop spaces
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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.
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