Convex and Concave Decompositions of Affine 3-Manifolds

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A (flat) affine 3-manifold is a 3-manifold with an atlas of charts to an affine space R3 with transition maps in the affine transformation group Aff(R3). 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 π-submanifolds and 2-convex affine manifolds, each of which is an irreducible 3-manifold. It follows that if there is no toral π-submanifold, then M is prime. Finally, we prove that if a closed affine manifold is covered by a connected open set in R3, then M is irreducible or is an affine Hopf manifold.
Publisher
SPRINGER HEIDELBERG
Issue Date
2020-03
Language
English
Article Type
Article
Citation

BULLETIN OF THE BRAZILIAN MATHEMATICAL SOCIETY, v.51, no.1, pp.243 - 291

ISSN
1678-7544
DOI
10.1007/s00574-019-00152-1
URI
http://hdl.handle.net/10203/272369
Appears in Collection
MA-Journal Papers(저널논문)
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