We prove that the homology of the mapping class groups of non-orientable surfaces stabilizes with the genus of the surface. Combining our result with recent work of Madsen and Weiss, we obtain thatâ€¦ (More)

The homology groups of the automorphism group of a free group are known to stabilize as the number of generators of the free group goes to infinity, and this paper relativizes this result to a familyâ€¦ (More)

The automorphisms of free groups with boundaries form a family of groups An,k closely related to mapping class groups, with the standard automorphisms of free groups as An,0 and (essentially) theâ€¦ (More)

Given a family of groups admitting a braided monoidal structure (satisfying mild assumptions) we construct a family of spaces on which the groups act and whose connectivity yields, via a classicalâ€¦ (More)

We provide a general method for finding all natural operations on the Hochschild complex of E-algebras, where E is any algebraic structure encoded in a prop with multiplication, as for example theâ€¦ (More)

We prove that the homology of the mapping class group of any 3manifold stabilizes under connected sum and boundary connected sum with an arbitrary 3-manifold when both manifolds are compact andâ€¦ (More)

We correct the proof of Theorem 5 of the paper Homology stability for outer automorphism groups of free groups, by the first two authors. AMS Classification 20F65; 20F28, 57M07

We give a complete and detailed proof of Harerâ€™s stability theorem for the homology of mapping class groups of surfaces, with the best stability range presently known. This theorem and its proof haveâ€¦ (More)

The framedn-discs operadf Dn is studied as semidirect product of SO(n) and the littlen-discs operad. Our equivariant recognition principle says that a grouplike space acted on by f Dn is equivalentâ€¦ (More)

The purpose of this note is to point out a gap in an argument in our paper [4] and explain how to fill it (or bypass it). The gap in [4] occurs in Section 4 in the proof of assertions (A) and (B), atâ€¦ (More)