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An arithmetic construction of the Gaussian and Eisenstein topographs

by Christopher David Shelley

Institution:	University of California – Santa Cruz
Department:	Mathematics
Degree:
Year:	2013
Keywords:	Mathematics; Forms; Geometry; Hermitian; Incidence; Quadratic; Topograph
Posted:
Record ID:	1996914
Full text PDF:	http://www.escholarship.org/uc/item/9mr7x65k

Abstract

We demonstrate a purely arithmetic construction of the Eisenstein and Gaussian topographs of Bestvina and Savin. Influenced by Conway's approach, we recover these topographs as incidence geometries over sets of ''generalized lax bases". We use the results of Johnson and Weiss to identify our constructions with the Coxeter geometries arising from projective general linear groups.