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Seiberg-Witten invariants, the topological degree and wall crossing formula

100%

Starostka M.

Open Mathematics

2012

tom 10

nr 6

2129-2137

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.

Some Results on Maps That Factor through a Tree

64%

Züst R.

Analysis and Geometry in Metric Spaces

2015

tom 3

nr 1

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 2/3, the map factors through a tree.

Ograniczanie wyników

1 Analysis and Geometry in Metric Spaces

1 Open Mathematics

1 Starostka M.

1 Züst R.

1 2015

1 2012

Wyniki wyszukiwania

Seiberg-Witten invariants, the topological degree and wall crossing formula

Some Results on Maps That Factor through a Tree