Flat cycles in the homology of \ SL / SO()
Grigori Avramidi
University of Chicago, USAT. Tâm Nguyên Phan
University of Chicago, USA
![Flat cycles in the homology of $\Gamma$ \ SL$_m \mathbb R$ / SO($m$) cover](/_next/image?url=https%3A%2F%2Fcontent.ems.press%2Fassets%2Fpublic%2Fimages%2Fserials%2Fcover-cmh.png&w=3840&q=90)
Abstract
In this paper we show that flat ()-dimensional tori give nontrivial rational homology cycles in congruence covers of the locally symmetric space SL \ SL / SO(). We also show that the dimension of the subspace of \ SL / SO(); spanned by flat -tori grows as one goes up in congruence covers.
Cite this article
Grigori Avramidi, T. Tâm Nguyên Phan, Flat cycles in the homology of \ SL / SO(). Comment. Math. Helv. 90 (2015), no. 3, pp. 645–666
DOI 10.4171/CMH/366