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On the cusped fan in a planar portrait of a manifold

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Please use this identifier to cite or link to this item:http://doi.org/10.14943/83966

Title: On the cusped fan in a planar portrait of a manifold
Authors: Kobayashi, Mahito Browse this author
Issue Date: 2006
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

Submitter: 数学紀要登録作業用

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