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Abstrakty
Planar portraits are geometric representations of smooth manifolds defined by their generic maps into the plane. A simple subclass called the polygonal portraits is introduced, their realisations, and relations of their shapes to the topology of source manifolds are discussed. Generalisations and analogies of the results to other planar portraits are also mentioned. A list of manifolds which possibly admit polygonal portraits is given, up to diffeomorphism and up to homotopy spheres. This article is intended to give a summary on our research on the topic, and hence precise proofs will be given in other papers.
Słowa kluczowe
Wydawca
Czasopismo
Rocznik
Tom
Strony
433--445
Opis fizyczny
Bibliogr. 20 poz., rys.
Twórcy
autor
- Department of Computer Science and Engineering Akita University 010-8502, Akita, Japan, mahito@math.akita-u.ac.jp
Bibliografia
- [1] J. Adem, Relations on iterated reduced powers, Proc. Nat. Acad. Set. U.S.A. 39 (1953), 636–638.
- [2] S. Blank, Extending immersions and regular homotopies in codim 1, Thesis, Brandeis University, 1967.
- [3] V. M. Buchstaber, T. E. Panov, Torus Actions and their Applications in Topology and Combinatorics, Univ. Lec. Series 24, Amer. Math. Soc., Providence, RI, 2002.
- [4] G. Francis, S. Troyer, Excellent maps with given folds and cusps in the plane, Houston J. Math. 3 (1977), 165–194, with Continuation: Excellent maps with given folds and cusps in the plane, Houston J. Math. 8 (1982), 53–60.
- [5] A. Haefliger, Quelques remarques sur les applications différentiables d’une surface dans le plan, Ann. Inst. Fourier (Grenoble) 10 (1960), 47–60.
- [6] D. Hacon, C. Mendes de Jesus, M. C. Romero Fuster, Fold maps from the sphere to the plane, Experiment. Math. 15 (2006), 491–497.
- [7] D. Hacon, C. Mendes de Jesus, M. C. Romero Fuster, Stable maps from surfaces to the plane with prescribed branching data, Topology Appl. 154 (2007), 166–175.
- [8] D. Hacon, C. Mendes de Jesus, M. C. Romero Fuster, Topological invariants of stable maps from a surface to the plane from a global viewpoint, in: Real and complex singularities, Lecture Notes in Pure and Appl. Math., 232, Dekker, New York, 2003, 227–235.
- [9] L. Kauffman, Planar surfaces immersions, Illionis J. Math. 23 (1979), 648–665.
- [10] M. Kobayashi, On the cusped fan in a planar portrait of a manifold, arXiv: math. GT/0703534v2.
- [11] M. Kobayashi, Transverse graphs to critical loci of stable maps into the plane, in preparation.
- [12] M. Kobayashi, Cores and planar portraits of homotopy sphere bundles over the circle, in preparation.
- [13] M. Kobayashi, Polygonal portraits of manifolds, in preparation.
- [14] M. Kobayashi, Manifolds admitting cyclic cores and their planar projections, in preparation.
- [15] H. Levine, Elimination of cusps, Topology 3, suppl. 2 (1965), 263–296.
- [16] H. Levine, Stable maps: an introduction with low dimensional examples, Bol. Soc. Brasil. Mat. 7 (1976), 145–184.
- [17] W. Neumann, S. Weintraub, Four-manifolds constructed via plumbing, Math. Ann. 238 (1978), 71–78.
- [18] T. Ohmoto, F. Aicardi, First order local invariants of apparent contours, Topology 45-1 (2006), 27–45.
- [19] R. Thom, Les singularités des applications différentiables, Ann. Inst. Fourier (Grenoble) 4 (1956), 43–87.
- [20] M. Yamamoto, Immersions of surfaces with boundary into the plane, Pacific J. Math. 212 (2003), 371–376.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-PWA4-0032-0009