Abelian monopoles: the case of a~positive-dimensional moduli space
Izvestiya. Mathematics , Tome 64 (2000) no. 1, pp. 193-206.

Voir la notice de l'article provenant de la source Math-Net.Ru

In this paper we consider (in the framework of the general Seiberg–Witten theory) the case when the moduli space of solutions of the Seiberg–Witten equations has positive even dimension. We describe a connection between the Seiberg–Witten invariants of a given manifold $X$ and those of the connected sum $Y=X \# d\overline{\mathbb{CP}}^2$ where $d=(1/2)\operatorname{v.dim}\mathcal M_{SW}$. We introduce the notion of a complex structure with degeneration (based on the connection between spinor geometry and complex geometry) and generalize the notion of a pseudoholomorphic curve to the case when the underlying manifold a priori has no almost complex structure.
@article{IM2_2000_64_1_a6,
     author = {N. A. Tyurin},
     title = {Abelian monopoles: the case of a~positive-dimensional moduli space},
     journal = {Izvestiya. Mathematics },
     pages = {193--206},
     publisher = {mathdoc},
     volume = {64},
     number = {1},
     year = {2000},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_2000_64_1_a6/}
}
TY  - JOUR
AU  - N. A. Tyurin
TI  - Abelian monopoles: the case of a~positive-dimensional moduli space
JO  - Izvestiya. Mathematics 
PY  - 2000
SP  - 193
EP  - 206
VL  - 64
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/IM2_2000_64_1_a6/
LA  - en
ID  - IM2_2000_64_1_a6
ER  - 
%0 Journal Article
%A N. A. Tyurin
%T Abelian monopoles: the case of a~positive-dimensional moduli space
%J Izvestiya. Mathematics 
%D 2000
%P 193-206
%V 64
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/IM2_2000_64_1_a6/
%G en
%F IM2_2000_64_1_a6
N. A. Tyurin. Abelian monopoles: the case of a~positive-dimensional moduli space. Izvestiya. Mathematics , Tome 64 (2000) no. 1, pp. 193-206. http://geodesic.mathdoc.fr/item/IM2_2000_64_1_a6/

[1] Donaldson S., “An application of gauge theory to four dimensional topology”, J. Diff. Geom., 18 (1983), 279–315 | MR | Zbl

[2] Donaldson S., “The Seiberg–Witten equations and 4-manifold topology”, Bulletin of the American mathematical society, 33:1 (1996), 45–70 | DOI | MR | Zbl

[3] Kronheimer P., Mrowka T., “The genus of embedded surfaces in the projective plane”, Math. Res. Lett., 1 (1994), 797–808 | MR | Zbl

[4] Kotschick D., Morgan J., Taubes C., “Four-manifolds without symplectic structures but with non trivial Seiberg–Witten invariants”, Math. Res. Lett., 2 (1995), 119–124 | MR | Zbl

[5] Taubes C., “The Seiberg–Witten invariants and symplectic forms”, Math. Res. Lett., 1 (1994), 809–822 | MR | Zbl

[6] Taubes C., “SW – Gr: from the Seiberg–Witten equations to pseudo-holomorphic curves”, J. Amer. Math. Soc., 9:3 (1996), 845–918 | DOI | MR | Zbl

[7] Tyurin N., “Neobkhodimoe i dostatochnoe uslovie deformatsii $B$-monopolya”, Izv. RAN. Ser. matem., 60:1 (1996), 211–224 | MR | Zbl

[8] Tyurin N., “Abelevy monopoli i kompleksnaya geometriya”, Matem. zametki, 65:3 (1998), 420–428 | MR

[9] Witten E., “Monopoles and four-manifolds”, Math. Res. Lett., 1 (1994), 769–789 | MR

[10] Wu W.-T., “Sur le classes caracteristique des structures fibrees spheriques”, Actual. Sci. Industr., 1183 (1952) | Zbl