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Examples of non-trivial roots of unity at ideal points of hyperbolic 3-manifolds
This paper gives examples of hyperbolic 3-manifolds whose SL(2,C) character
varieties have ideal points whose associated roots of unity are not 1 or -1.
This answers a question of Cooper, Culler, Gillet, Long, and Shalen as to
whether roots of unity other than 1 and -1 occur.Comment: 12 pages, 1 figure, LaTeX2e. Minor changes, additional remarks, new
description of 2nd example. To appear in_Topology
Dialectical Teaching Strategies for First and Second-Year Students
An oppositional or bi-polar understanding of meaning (Rychlak, 1976). This ancient understanding of meaning has many applications for instructors.https://digitalscholarship.unlv.edu/btp_expo/1020/thumbnail.jp
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