Abstract
My purpose here is to give some background to a series of sculptures I have been creating in which nonorientable surfaces, especially crosscaps, play a mathematical content role. The fundamental circle of theorems involved is on the classification of surfaces in terms of handles and crosscaps. The most basic examples are spheres, tori, mobius bands, projective planes, and klein bottles, cf., [CF1, HF1] for discussion of my earlier sculpture involving these concepts. For an exposition and further references to the mathematical background for the circle of theorems I refer to, see [FG1].
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