Sandwich type theorems
Seiberg-Witten invariants, the topological degree and wall crossing formula
Following S. Bauer and M. Furuta we investigate finite dimensional approximations of a monopole map in the case b 1 = 0. We define a certain topological degree which is exactly equal to the Seiberg-Witten invariant. Using homotopy invariance of the topological degree a simple proof of the wall crossing formula is derived.
Sequences of fixed point indices of iterations in dimension 2.
Solvability Of Operator Equations And Periodic Solutions Of Semilinear Hyperbolic Equations
Solving Systems of Polynomial Equations by Bounded and Real Homotopy.
Some applications of the topological degree theory to multi-valued boundary value problems [Book]
Some combinatorial results about the operators with jumping nonlinearities
Some elementary applications of topological degree.
Some Results on Maps That Factor through a Tree
We give a necessary and sufficient condition for a map deffned on a simply-connected quasi-convex metric space to factor through a tree. In case the target is the Euclidean plane and the map is Hölder continuous with exponent bigger than 1/2, such maps can be characterized by the vanishing of some integrals over winding number functions. This in particular shows that if the target is the Heisenberg group equipped with the Carnot-Carathéodory metric and the Hölder exponent of the map is bigger than...