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On the cusped fan in a planar portrait of a manifold
| Title: | On the cusped fan in a planar portrait of a manifold |
| Authors: | Kobayashi, Mahito Browse this author |
| Issue Date: | 2006 |
| Publisher: | Department of Mathematics, Hokkaido University |
| Journal Title: | Hokkaido University Preprint Series in Mathematics |
| Volume: | 816 |
| Start Page: | 1 |
| End Page: | 25 |
| Abstract: | As a way to draw a picture of a manifold in the plane, we consider to take the image of the manifold through a stable map. We call the image, paired with the critical values, the planar portrait of a manifold. The cusped fan is its basic local con guration. In this article, we focus on the breing structure over the cusped fan, and give its characterisation. As application, the source manifolds of certain planar portraits are characterised, and stable maps of closed manifolds such as the projective plane kP 2 (k = R;C;H), regular complex toric surfaces, and some sphere bundles over spheres etc. are constructed. As a biproduct, we obtain an in nite to one correspondence of projections up to right-left equivalence, of a xed manifold to a planar portrait. Further applications on characterising manifolds by planar portraits are left to our forthcomming papers. |
| Type: | bulletin (article) |
| URI: | http://hdl.handle.net/2115/69624 |
| Appears in Collections: | 理学院・理学研究院 (Graduate School of Science / Faculty of Science) > Hokkaido University Preprint Series in Mathematics
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Submitter: 数学紀要登録作業用
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