NEW TOPOLOGICAL INVARIANTS FOR REAL- AND ANGLE-VALUED MAPS: AN ALTERNATIVE TO MORSE-NOVIKOV THEORY

These invariants are on one side analogues of rest points, instantons and closed trajectories of vector fields and on the other side, refine basic topological invariants like homology and monodromy. They are associated to tame maps, considerably more general than Morse maps, that are defined on spaces which are considerably more general than manifolds. They are computable by computer implementable algorithms and have strong robustness properties. They relate the dynamics of flows that admit the map as "Lyapunov map" to the topology of the underlying space, in a similar manner as Morse Novikov theory does.

Readership: Graduate students and researchers in geometry and topology, topologists, geometers, experts in dynamics, computer scientists and data analysts.