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Convex and concave decompositions of aff...
Choi, Suhyoung...

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Convex and concave decompositions of affine $3$-manifolds by Choi, Suhyoung ( Author )
Lemonjar Open Access
Australian National University
06-09-2023
A (flat) affine $3$-manifold is a $3$-manifold with an atlas of charts to an affine space $\mathbb{R}^3$ with transition maps in the affine transformation group $\mathrm{Aff}(\mathbb{R}^3)$. We will show that a connected closed affine $3$-manifold is either an affine Hopf $3$-manifold or decomposes canonically to concave affine submanifolds with incompressible boundary, toral $\pi$-submanifolds and $2$-convex affine manifolds, each of which is an irreducible $3$-manifold. It follows that if there is no toral $\pi$-submanifold, then $M$ is prime. Finally, we prove that if a closed affine manifold is covered by a domain in $\mathbb{R}^{n}$, then $M$ is irreducible or is an affine Hopf manifold.
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Article
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29.34 KB
English
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MYR 0.01
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http://arxiv.org/abs/1411.1273
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