DC Field | Value | Language |
---|---|---|
dc.contributor.author | Choi, Suhyoung | ko |
dc.date.accessioned | 2013-03-04T17:31:26Z | - |
dc.date.available | 2013-03-04T17:31:26Z | - |
dc.date.created | 2012-02-06 | - |
dc.date.created | 2012-02-06 | - |
dc.date.created | 2012-02-06 | - |
dc.date.issued | 2001-11 | - |
dc.identifier.citation | MEMOIRS OF THE AMERICAN MATHEMATICAL SOCIETY, v.154, no.730, pp.1 - 1 | - |
dc.identifier.issn | 0065-9266 | - |
dc.identifier.uri | http://hdl.handle.net/10203/83464 | - |
dc.description.abstract | An affine manifold is a manifold with torsion-free flat affine connection. A geometric topologist's definition of an affine manifold is a manifold with an atlas of charts to the affine space with affine transition functions; a radiant affine manifold is an affine manifold with a holonomy group consisting of affine transformations fixing a common fixed point. We decompose a closed radiant affine 3-manifold into radiant 2-convex affine manifolds and radiant concave affine 3-manifolds along mutually disjoint totally geodesic tori or Klein bottles using the convex and concave decomposition of real projective n-manifolds developed earlier. Then we decompose a 2-convex radiant affine manifold into convex radiant affine manifolds and concave-cone affine manifolds. To do this, we will obtain certain nice geometric objects in the Kuiper completion of a holonomy cover. The equivariance and local finiteness property of the collection of such objects will show that their union covers a compact submanifold of codimension zero, the complement of which is convex. Finally, using the results of Barbot, we will show that a closed radiant affine 3-manifold admits a total cross-section, confirming a conjecture of Carriere, and hence every closed radiant affine 3-manifold is homeomorphic to a Seifert fibered space with trivial Euler number, or a virtual bundle over a circle with fiber homeomorphic to a Euler characteristic zero surface. In Appendix C, Thierry Barbot and the author show the nonexistence of certain radiant affine 3-manifolds and that compact radiant affine 3-manifolds with nonempty totally geodesic boundary admit total cross-sections, which are key results for the main part of the paper. | - |
dc.language | English | - |
dc.publisher | AMER MATHEMATICAL SOC | - |
dc.title | The Decomposition and Classification of Radiant Affine 3-Manifolds | - |
dc.type | Article | - |
dc.identifier.wosid | 000170649200001 | - |
dc.identifier.scopusid | 2-s2.0-0041077630 | - |
dc.type.rims | ART | - |
dc.citation.volume | 154 | - |
dc.citation.issue | 730 | - |
dc.citation.beginningpage | 1 | - |
dc.citation.endingpage | 1 | - |
dc.citation.publicationname | MEMOIRS OF THE AMERICAN MATHEMATICAL SOCIETY | - |
dc.contributor.localauthor | Choi, Suhyoung | - |
dc.description.isOpenAccess | N | - |
dc.type.journalArticle | Article | - |
dc.subject.keywordAuthor | real projective structure | - |
dc.subject.keywordAuthor | affine 3-manifold | - |
dc.subject.keywordAuthor | affine structure | - |
dc.subject.keywordAuthor | geometric structure | - |
dc.subject.keywordAuthor | flat connection | - |
dc.subject.keywordAuthor | flow | - |
dc.subject.keywordAuthor | foliation | - |
dc.subject.keywordPlus | REAL PROJECTIVE-STRUCTURES | - |
dc.subject.keywordPlus | CONVEX DECOMPOSITIONS | - |
dc.subject.keywordPlus | COMPACT SURFACES | - |
dc.subject.keywordPlus | MANIFOLDS | - |
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