Tuesday
5
February
2019

Speaker:
Hosana Valimbavaka Ranaivomanana

Time:
14:00

Venue:
Room 1006, Mathematical Sciences/Industrial Psychology

My thesis investigates the relationship between the handle element of the De Rham cohomology algebra of a compact oriented smooth manifold, thought of as a Frobenius algebra, and the Euler class of the manifold. In this way it gives a complete answer to an exercise posed in the monograph of Kock (which is based on a paper of Abrams), where one is asked to show that these two classes are equal. Firstly, an overview of De Rham cohomology, Thom and Euler classes of smooth manifolds, PoincarĂ© duality, Frobenius algebras, and their graphical calculus is given. Finally, it is shown that the handle element and the Euler class are indeed equal for even-dimensional manifolds. However, they are not equal for odd-dimensional manifolds.