Publication: Minkowski’s Conjecture, Well-Rounded Lattices and Topological Dimension
Open/View Files
Date
2005
Authors
Published Version
Journal Title
Journal ISSN
Volume Title
Publisher
American Mathematical Society
The Harvard community has made this article openly available. Please share how this access benefits you.
Citation
McMullen, Curtis T. 2005. Minkowski’s conjecture, well-rounded
lattices and topological dimension. Journal of the American Mathematical Society 18: 711-734. Revised 2007.
Research Data
Abstract
Let A ⊂ SLn(R) be the diagonal subgroup, and identify SLn(R)/SLn(Z)with the space of unimodular lattices in Rn. In this paper we show that the closure of any bounded orbit A • L ⊂ SLn(R)/SLn(Z)meets the set of well-rounded lattices. This assertion implies Minkowski's conjecture for n=6 and yields bounds for the density of algebraic integers in totally real sextic fields.
The proof is based on the theory of topological dimension, as reflected in the combinatorics of open covers of Rn and Tn.
Description
Other Available Sources
Keywords
Terms of Use
This article is made available under the terms and conditions applicable to Other Posted Material (LAA), as set forth at Terms of Service