Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS
   
Mobile Device Pairing
Green Open Access
Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Vector fields on polyhedra


Author: Michael A. Penna
Journal: Trans. Amer. Math. Soc. 232 (1977), 1-31
MSC: Primary 57D25; Secondary 58D99
MathSciNet review: 0451258
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 57D25, 58D99

Retrieve articles in all journals with MSC: 57D25, 58D99


Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1977-0451258-6
PII: S 0002-9947(1977)0451258-6
Keywords: Polyhedron, manifold, tangent bundle, vector field, Hopf's theorem, Gauss-Bonnet formula
Article copyright: © Copyright 1977 American Mathematical Society