Equivariant Morse Theory and the Yang-Mills Equation on Riemann Surfaces

1980 ◽  
pp. 11-22
Author(s):  
Raoul Bott
Keyword(s):  
Morse Theory ◽  
Riemann Surfaces ◽  
Yang Mills

The Yang-Mills equations over Riemann surfaces

1983 ◽  
Vol 308 (1505) ◽  
pp. 523-615 ◽  
Keyword(s):  
Riemann Surface ◽  
Gauge Symmetry ◽  
Moduli Space ◽  
Morse Theory ◽  
Riemann Surfaces ◽  
Point Of View ◽  
Yang Mills ◽  
Critical Sets

The Yang-Mills functional over a Riemann surface is studied from the point of view of Morse theory. The main result is that this is a ‘perfect' functional provided due account is taken of its gauge symmetry. This enables topological conclusions to be drawn about the critical sets and leads eventually to information about the moduli space of algebraic bundles over the Riemann surface. This in turn depends on the interplay between the holomorphic and unitary structures, which is analysed in detail.

scholarly journals Non-supersymmetric matrix strings from generalized Yang–Mills theory on arbitrary Riemann surfaces

2000 ◽  
Vol 576 (1-3) ◽  
pp. 241-264 ◽  
Author(s):  
M. Billó ◽  
A. D'Adda ◽  
P. Provero
Keyword(s):  
Riemann Surfaces ◽  
Yang Mills

scholarly journals Morse theory and non-minimal solutions to the Yang-Mills equations

1997 ◽  
Vol 21 (3) ◽  
pp. 567-593
Author(s):  
Hong-Yu Wang
Keyword(s):  
Morse Theory ◽  
Yang Mills

Yang?Mills instantons over Riemann surfaces

1992 ◽  
Vol 24 (4) ◽  
pp. 275-281 ◽  
Author(s):  
M. Lled� ◽  
I. Mart�n ◽  
A. Restuccia ◽  
A. Mendoza
Keyword(s):  
Riemann Surfaces ◽  
Yang Mills

MODULI OF STABLE PAIRS FOR HOLOMORPHIC BUNDLES OVER RIEMANN SURFACES

1991 ◽  
Vol 02 (05) ◽  
pp. 477-513 ◽  
Author(s):  
STEVEN B. BRADLOW ◽  
GEORGIOS D. DASKALOPOULOS
Keyword(s):  
Moduli Space ◽  
Riemann Surfaces ◽  
Holomorphic Section ◽  
Stable Bundles ◽  
Space Problem ◽  
Yang Mills ◽  
Closed Riemann Surface ◽  
Holomorphic Bundles ◽  
Stable Pairs ◽  
Compact Kähler Manifold

It this paper we study the space of gauge equivalence classes of pairs [Formula: see text] where [Formula: see text] represents a holomorphic structure on a complex bundle, E, over a closed Riemann Surface, and ϕ is a holomorphic section. We define a space of stable pairs and consider the moduli space problem for this space. The space of stable pairs, [Formula: see text], is related to the space of solution to the Vortex (Hermitian-Yang-Mills-Higgs) equation. Using the parameter, τ, which appears in this equation we can define subspaces [Formula: see text] within [Formula: see text]. We show that under suitable restrictions on τ and the degree of E, the space [Formula: see text] is naturally a finite dimensional, Hausdorff, compact Kähler manifold. We show further that there is a natural holomorphic map from this space onto the Seshadri compactification of the moduli space of stable bundles and that this map is generically a fibration.

scholarly journals Antiperfection of Yang–Mills Morse theory over a nonorientable surface

2015 ◽  
Vol 26 (11) ◽  
pp. 1550087
Author(s):  
Thomas John Baird
Keyword(s):  
Morse Theory ◽  
Betti Numbers ◽  
Nonorientable Surface ◽  
Yang Mills ◽  
Moduli Stack

We use Morse theory of the Yang–Mills functional to compute the Betti numbers of the moduli stack of flat U(3)-bundles over a compact nonorientable surface. Our result establishes the antiperfection conjecture of Ho–Liu, and establishes the equivariant formality conjecture of the author for U(3)-bundles.

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