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University Park
Altoona

Friday, February 13, 2009
4:00 pm, 260 Hawthorn

Zhaohu Nie
Penn State Altoona

Secondary Chern-Euler classes.

Abstract: This is a continuation of our last talk. I will review the definition of the secondary Chern-Euler form, defined on the restriction of the sphere bundle on a submanifold. If the submanifold has codimension 1, we give detail to show that the form is exact away from the outward and inward unit normal vectors. Using Stokes' theorem, this then evaluates the pairing of the secondary Chern-Euler form with the image of the submanifold under any non-zero vector field. If the submanifold has codimension bigger than 1, we will give some conceptual proofs that the pairing of the class with the unit normal sphere bundle of the submanifold compute the Euler characteristic of the submanifold.

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We meet weekly on Friday afternoons at Penn State Altoona (and sometimes at Penn State University Park). If you are interested in giving a talk in our seminar please contact one of the coordinators for the Spring 2009 semester: Wojtek Dorabiala and Aissa Wade.

 

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