منابع مشابه
Homological Infiniteness of Torelli Groups
1 → I g,r → M n g,r → Sp(2g,Z) → 1. We omit the decorations n and r when they are zero. In a series of papers [7, 8, 9, 10], D. Johnson obtained several fundamental results concerning the structure of Ig and Ig,1 (see also [11, 2]). In particular, he proved that Ig and Ig,1 are finitely generated for all g ≥ 3. On the contrary, A. Miller and D. McCullough [14] showed that I2 (and hence I n 2,r ...
متن کاملInfinitesimal Presentations of the Torelli Groups
Contents 1. Introduction 597 2. Braid groups in positive genus 601 3. Relative completion of mapping class groups 603 4. Mixed Hodge structures on Torelli groups 608 5. Review of continuous cohomology 613 6. Remarks on the representations of sp g 616 7. Continuous cohomology of Torelli groups 618 8. The lower central series quotients of a surface group 621 9. The action of t 1 g on p g 623 10. ...
متن کاملDigital cohomology groups of certain minimal surfaces
In this study, we compute simplicial cohomology groups with different coefficients of a connected sum of certain minimal simple surfaces by using the universal coefficient theorem for cohomology groups. The method used in this paper is a different way to compute digital cohomology groups of minimal simple surfaces. We also prove some theorems related to degree properties of a map on digital sph...
متن کاملCutting and Pasting in the Torelli Groups
We introduce machinery to allow “cut-and-paste”-style inductive arguments in the Torelli subgroups of the mapping class groups. In the past these arguments have been problematic because restricting the Torelli groups to subsurfaces gives different groups depending on how the subsurfaces are embedded. We define a category TSur whose objects are surfaces together with a decoration restricting how...
متن کاملLectures on the Cohomology of Groups
The cohomology theory of groups arose from both topological and algebraic sources. The starting point for the topological aspect of the theory was a 1936 paper by Hurewicz [7], in which he introduced aspherical spaces. These are spaces X such that πn(X) = 0 for n 6= 1. (Hurewicz had introduced higher homotopy groups just one year earlier, and he was now trying to understand the spaces with the ...
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: Forum of Mathematics, Pi
سال: 2020
ISSN: 2050-5086
DOI: 10.1017/fmp.2020.5