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Search: MSC category 57R57 ( Applications of global analysis to structures on manifolds, Donaldson and Seiberg-Witten invariants [See also 58-XX] )

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1. CJM 2001 (vol 53 pp. 1309)

Steer, Brian; Wren, Andrew
The Donaldson-Hitchin-Kobayashi Correspondence for Parabolic Bundles over Orbifold Surfaces
A theorem of Donaldson on the existence of Hermitian-Einstein metrics on stable holomorphic bundles over a compact K\"ahler surface is extended to bundles which are parabolic along an effective divisor with normal crossings. Orbifold methods, together with a suitable approximation theorem, are used following an approach successful for the case of Riemann surfaces.

Categories:14J17, 57R57

2. CJM 2000 (vol 52 pp. 293)

Collin, Olivier
Floer Homology for Knots and $\SU(2)$-Representations for Knot Complements and Cyclic Branched Covers
In this article, using 3-orbifolds singular along a knot with underlying space a homology sphere $Y^3$, the question of existence of non-trivial and non-abelian $\SU(2)$-representations of the fundamental group of cyclic branched covers of $Y^3$ along a knot is studied. We first use Floer Homology for knots to derive an existence result of non-abelian $\SU(2)$-representations of the fundamental group of knot complements, for knots with a non-vanishing equivariant signature. This provides information on the existence of non-trivial and non-abelian $\SU(2)$-representations of the fundamental group of cyclic branched covers. We illustrate the method with some examples of knots in $S^3$.

Categories:57R57, 57M12, 57M25, 57M05

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