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Topology/Geometry Seminar
Thursday, October 12, 2006
5:05pm,
106 McAllister
Gordana Stojanovic
Penn State
Totally skew embeddings and their generalizations.
Abstract: A submanifold M of an affine space is called totally skew if any two lines, tangent to M at two distinct points, are neither parallel nor intersecting. The following is a natural question: for a given smooth manifold M what is the smallest dimension of an affine space that can contain M as a totally skew submanifold? This simple, but nontrivial question is related to some well studied problems in algebraic topology. I will define a generalization of the totally skew embeddings, so-called embeddings wih multiple regularity, which also generalize a certain other class of maps defined in the context of approximation theory. I will survey some of the available results on the subject and if time permits, I will also discuss some other close relatives, such as skew maps and T-embeddings.
We meet weekly on Thursday afternoons, with the third meeting of each month in Altoona. If you are interested in giving a talk in our seminar please contact one of the coordinators for the Spring 2006 semester: Aissa Wade and Wojciech Dorabiala.
