The Dehn function of $\mathrm{SL}(n;\mathbb{Z})$ | Annals of Mathematics

Abstract We prove that when n≥5, the Dehn function of SL(n;ℤ) is quadratic. The proof involves decomposing a disc in SL(n;ℝ)/SO(n) into triangles of varying sizes. By mapping these triangles into SL(n;ℤ) and replacing large elementary matrices by “shortcuts,” we obtain words of a particular form, and we use combinatorial techniques to fill these loops.

KEYWORDS

SHARE & LIKE

数学年刊（Annals of Mathematics）

0 Following 0 Fans 0 Projects 674 Articles

SIMILAR ARTICLES

Abstract For any nondegenerate, quasi-homogeneous hypersurface singularity, we describe a family of moduli spaces, a virtual cycle, and a correspondin

Abstract For a large class of nonlinear Schrödinger equations with nonzero conditions at infinity and for any speed c less than the sound velocity, we

Abstract Let L2,p(ℝ2) be the Sobolev space of real-valued functions on the plane whose Hessian belongs to Lp. For any finite subset E⊂ℝ2 and p>2, let

Abstract We prove that for any group G in a fairly large class of generalized wreath product groups, the associated von Neumann algebra LG completely

Abstract We study the parity of 2-Selmer ranks in the family of quadratic twists of an arbitrary elliptic curve E over an arbitrary number field K. We

Abstract This paper has two main results. Firstly, we complete the parametrisation of all p-blocks of finite quasi-simple groups by finding the so-cal

Abstract We derive sharp Moser-Trudinger inequalities on the CR sphere. The first type is in the Adams form, for powers of the sublaplacian and for ge