A Gauss-Ostrogradskii theorem for integral transforms over the euler characteristic

Abstract

We prove an analog of the Gauss-Ostrogradskii theorem for integration over the Euler characteristic, expressing the Euler characteristic of a manifold with a boundary in terms of the zeros of a smooth dynamical system and its behaviour on the boundary. This result makes is possible to compute the Euler characteristic of a closed manifold via behaviour of a discontinuous dynamical system. The Gauss-Ostrogradskii theorem for the Euler characteristic also clarifies certain classial computations.

Keywords:

• Euler characteristic
• discontinuous dynamical system
• integral transform

MSC(1991):

• 35A22
• 35A30

Additional information

Notes on contributors

Aleksandr V. Pukhlikov