Abstract
This paper presents a bundle theory for studying vector fields and their integral flows on polyhedra ∗ _ \ast and applications. Every polyhedron has a tangent object in the category of simplicial bundles in much the same way as every smooth manifold has a tangent object in the category of smooth vector bundles. One can show that there is a correspondence between piecewise smooth flows on a polyhedron P and sections of the tangent object of P (i.e., vector fields on P); using this result one can prove existence results for piecewise smooth flows on polyhedra. Finally an integral formula for the Euler characteristic of a closed, oriented, even-dimensional combinatorial manifold is given; as a consequence of this result one obtains a representation of Euler classes of such combinatorial manifolds in terms of piecewise smooth forms.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.