On the homotopy of the stable mapping class group

@article{Tillmann1997OnTH,
  title={On the homotopy of the stable mapping class group},
  author={U. Tillmann},
  journal={Inventiones mathematicae},
  year={1997},
  volume={130},
  pages={257-275}
}
  • U. Tillmann
  • Published 1997
  • Mathematics
  • Inventiones mathematicae
Abstract. By considering all surfaces and their mapping class groups at once, it is shown that the classifying space of the stable mapping class group after plus construction, BΓ∞+, has the homotopy type of an infinite loop space. The main new tool is a generalized group completion theorem for simplicial categories. The first deloop of BΓ∞+ coincides with that of Miller [M] induced by the pairs of pants multiplication. The classical representation of the mapping class group onto Siegel's… Expand
COHOMOLOGY OF THE STABLE MAPPING CLASS
Topology, Geometry and Quantum Field Theory: Cohomology of the stable mapping class group
Homotopy type of a 2-category
The low-dimensional homotopy of the stable mapping class group
The stable mapping class group of simply connected 4-manifolds
Strings and the Stable Cohomology of Mapping Class Groups
Homological stability for the mapping class groups of non-orientable surfaces
Stabilization for the automorphisms of free groups with boundaries
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