Affine Winding Numbers and Their Applications to the Study of Front Propagation

Let M be an oriented manifold. We study the question how many times a wave front W on M has passed through a given point p ∈ M . Namely, we introduce the numerical topological invariant winp(W (t)) such that winp(W (t1)) − winp(W (t2)) is the algebraic number of times the wave front W passed through p between the time moments t1 and t2. This invariant… CONTINUE READING