On the second homology group of the Torelli subgroup of AutpFnq
نویسندگان
چکیده
Let IAn be the Torelli subgroup of AutpFnq. We give an explicit finite set of generators for H2pIAnq as a GLnpZq-module. Corollaries include a version of surjective representation stability for H2pIAnq, the vanishing of the GLnpZq-coinvariants of H2pIAnq, and the vanishing of the second rational homology group of the level l congruence subgroup of AutpFnq. Our generating set is derived from a new group presentation for IAn which is infinite but which has a simple recursive form.
منابع مشابه
A Birman exact sequence for the Torelli subgroup of AutpFnq
We develop an analogue of the Birman exact sequence for the Torelli subgroup of AutpFnq. This builds on earlier work of the authors who studied an analogue of the Birman exact sequence for the entire group AutpFnq. These results play an important role in the authors’ recent work on the second homology group of the Torelli group.
متن کاملA Birman exact sequence for the Torelli subgroup of Aut(Fn)
We develop an analogue of the Birman exact sequence for the Torelli subgroup of AutpFnq. This builds on earlier work of the authors who studied an analogue of the Birman exact sequence for the entire group AutpFnq. These results play an important role in the authors’ recent work on the second homology group of the Torelli group.
متن کاملThe second rational homology group of the moduli space of curves with level structures
Let Γ be a finite-index subgroup of the mapping class group of a closed genus g surface that contains the Torelli group. For instance, Γ can be the level L subgroup or the spin mapping class group. We show that H2(Γ;Q)∼=Q for g≥ 5. A corollary of this is that the rational Picard groups of the associated finite covers of the moduli space of curves are equal to Q. We also prove analogous results ...
متن کاملGenerating the Torelli Group
We give a new proof of the theorem of Birman–Powell that the Torelli subgroup of the mapping class group of a closed orientable surface of genus at least 3 is generated by simple homeomorphisms known as bounding pair maps. The key ingredient is a proof that the subcomplex of the curve complex of the surface spanned by curves within a fixed homology class is connected.
متن کاملA Birman exact sequence for AutpFnq
The Birman exact sequence describes the effect on the mapping class group of a surface with boundary of gluing discs to the boundary components. We construct an analogous exact sequence for the automorphism group of a free group. For the mapping class group, the kernel of the Birman exact sequence is a surface braid group. We prove that in the context of the automorphism group of a free group, ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2015