Fundamental Group of Self-Dual Four-Manifolds with Positive Scalar Curvature

Details Fundamental Group of Self-Dual Four-Manifolds with Positive Scalar Curvature Fundamental Group of Self-Dual Four-Manifolds with Positive Scalar Curvature

1995-03-28

arxiv.org/abs/dg-ga/9503013v1

Mathematics

Differential Geometry

plain TEX; mathchar.tex and definiti.tex are available from dg-ga, and vanilla.sty follows the paper

Scientific paper

Main Theorem (3.3): Let $M$ be a compact four-dimensional manifold either with curvature, positive on complex isotropic two-planes, or self-dual of positive scalar curvature. If $\pi_1 (M)$ admits a nontrivial unitary representation, and $M$ is orientable, then there exists a surjective homomorphism from $\pi_1 (M)$ on $\bbz$. Corollary: If $\pi_1 (M)$ is finite, then either $\pi_1 (M) = 1$, or $\pi_1 (M) = \bbz_2$. Observe that finitely presented groups which do not admit a nontrivial unitary representation, are extremely rare (see 3.4).

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