Browsing by Subject "group theory"
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Item Computational Methods for Investigating Higher Teichmüller Spaces(2020-11) Malik, Arjun; Stecker, FlorianThis paper deals with the discrete subgroup problem, solvable through the study of higher Teichmüller theory. The discrete subgroup problem is as follows: given a Lie group (a group with continuity) such as R, how do you find discrete subgroups, such as Z, particularly those of a type similar to (isomorphic to) a certain group? This paper details how, using theorems pertaining to Higher Teichmüller theory graphing the eigenvalue gaps of a matrix group can be used to figure out if it is a discrete subgroup of a Lie Group. In it, I find two subsets of results: one is working towards an attempt to validate recently found results about a Lie group, and the other is a result about the method itself (specifically, projective convex bending) and how it can be used empirically.Item Solutions to problems 1-67 in Dynamical theory of groups and fields(1963) DeWitt, Bryce S. (Bryce Seligman), 1923-2004