Index Classes for Vector Fields and Their Relation to Certain Characteristic Classes

Journal article, 2013

While studying vector fields on manifolds with boundary there are three important indexes to consider. We construct three cohomology classes to compute these. We relate these classes to other classes, the relative Euler class as defined by Sharafutdinov and the secondary Chern-Euler class as defined by Sha. Our results also yield a new proof of the Poincare-Hopf index theorem.