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Fundamental Group of Self-Dual Four-Manifolds with Positive Scalar Curvature by Reznikov, Alexander G. is a scholarly article available to read on EtoBox.

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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).

Author

Reznikov, Alexander G.

Published

1995

Language

EN