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

• Autorzy: Maciej Starostka
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

Wall crossing formula; Seiberg-Witten invariants; Bauer-Furuta invariants; Monopole map; Topological degree

Kategorie tematyczne

• 55M25: Degree, winding number
• 57R57: Applications of global analysis to structures on manifolds, Donaldson and Seiberg-Witten invariants

• Wydawca: De Gruyter Open
• Czasopismo: Open Mathematics
• Rocznik: 2012
• Tom: 10
• Numer: 6
• Strony: 2129-2137

Daty

wydano

2012-12-01

online

2012-10-12

Twórcy

autor

Maciej Starostka

• Faculty of Technical Physics and Applied Mathematics, Gdańsk University of Technology, Narutowicza 11/12, 80-233, Gdańsk, Poland

Bibliografia

• [1] Bauer S., Furuta M., A stable cohomotopy refinement of Seiberg-Witten invariants I, Invent. Math., 2004, 155(1), 1–19 http://dx.doi.org/10.1007/s00222-003-0288-5[Crossref]
• [2] Bott R., Tu L.W., Differential Forms in Algebraic Topology, Grad. Texts in Math., 82, Springer, New York-Berlin, 1982
• [3] tom Dieck T., Transformation Groups, de Gruyter Stud. Math., 8, Walter de Gruyter, Berlin, 1987 http://dx.doi.org/10.1515/9783110858372[Crossref]
• [4] Salamon D.A., Spin Geometry and Seiberg-Witten Invariants, unpublished manuscript
• [5] Taubes C.H., Differential Geometry, Oxf. Grad. Texts Math., 23, Oxford University Press, New York, 2011

Identyfikatory

DOI

10.2478/s11533-012-0125-4