Superrigidity, arithmeticity, normal subgroups: results, ramifications and directions
David Fisher
TL;DR
This paper explores the implications and open questions related to Margulis' theorems on superrigidity, arithmeticity, and normal subgroups, highlighting their significance in the field of mathematics.
Contribution
It provides a comprehensive overview of the ramifications of Margulis' key theorems and identifies open problems inspired by his work and historical context.
Findings
Highlights the importance of Margulis' theorems in modern mathematics
Identifies open questions and future research directions
Connects historical development with current mathematical challenges
Abstract
This essay points to many of the interesting ramifications of Margulis' arithmeticity theorem, the superrigidity theorem, and normal subgroup theorem. We provide some history and background, but the main goal is to point to interesting open questions that stem directly or indirectly from Margulis' work and it's antecedents.
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Taxonomy
TopicsAdvanced Topology and Set Theory · Algebraic Geometry and Number Theory · Homotopy and Cohomology in Algebraic Topology