Stabilization for the automorphisms of free groups with boundaries
نویسندگان
چکیده
منابع مشابه
Stabilization for the Automorphisms of Free Groups with Boundaries
There is by now a significant literature on homological stability properties of various families of discrete groups, including matrix groups, mapping class groups of surfaces, and automorphism groups of free groups. The present paper is yet another contribution in this direction, for a family of groups An,k that can be thought of as relative versions of automorphism groups of free groups. These...
متن کاملAutomorphisms of Free Groups with Boundaries
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) the symmetric automorphisms of free groups as A0,k . We construct a contractible space Ln,k on which An,k acts with finite stabilizers and finite quotient space and deduce a range for the virtual cohomolog...
متن کاملErratum to “Stabilization for the automorphisms of free groups with boundaries”
The gap in [5] occurs in Section 4 in the proof of assertions (A) and (B), at the point where there are diagram chasing arguments in two commutative diagrams (displayed on page 1333 for case (A)). In each diagram the groups Gn in the two rows are isomorphic but not identical. If we denote by Gn and G n these two isomorphic groups, the first diagram chase needs the composition Hi.Gn/!Hi.GnC1/!Hi...
متن کاملErratum to “stabilization for the Automorphisms of Free Groups with Boundaries” Allen Hatcher and Nathalie Wahl
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), at the point where there are diagram chasing arguments in two commutative diagrams (displayed on page 1333 for case (A)). In each diagram the groupsGn in the two rows are isomorphic but not identical....
متن کاملStabilization for the Automorphisms of Free Groups with Boundaries, Ii Allen Hatcher and Nathalie Wahl
In this follow-up to our earlier paper [6], we improve substantially the dimension range of the homology stability results for mapping class groups of general 3-manifolds, and at the same time bypass a gap in that paper. The new results, stated as Theorems 2.1–2.5, have a stable dimension range of slope 2 rather than slope 3. They arise from a new technique vaguely reminiscent of an h-principle...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Geometry & Topology
سال: 2005
ISSN: 1364-0380,1465-3060
DOI: 10.2140/gt.2005.9.1295