Tight Surfaces in Three-Dimensional Compact Euclidean Space Forms
January 24, 2008
Bailey Hall 207
A surface in space is tight if any plane cuts it into at most two pieces. A classification of tight surfaces was carried out at the end of the 20th century that culminated in an unusual example of a tight polyhedral surface for which there is no smooth counterpart. More recently, this study has been extended to surfaces immersed in more exotic spaces, and in particular the compact Euclidean space forms (these are quotient spaces of Euclidean 3-space by a freely acting discrete subgroup of the Euclidean group). In this talk we describe these spaces geometrically, develop the notation of tightness for them, and illustrate (through interactive computer graphics) a number of unexpected examples of tight surfaces that can be found within them.
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