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Equivariant, Almost-arborescent Representations of Open Simply-connected 3-manifolds: A Finiteness Result (Memoirs of the American Mathematical Society) - Paperback

2004, ISBN: 0821834606

Mass Market Paperback, [EAN: 9780821834602], American Mathematical Society, American Mathematical Society, Book, [PU: American Mathematical Society], 2004-03-30, American Mathematical Society, 278329, Applied Mathematics, 922530, Mathematical Modelling, 278335, Mathematics for Scientists & Engineers, 278419, Physics, 278320, Mathematics, 57, Science & Nature, 1025612, Subjects, 266239, Books, 278353, Geometry & Topology, 278320, Mathematics, 57, Science & Nature, 1025612, Subjects, 266239, Books, 922942, Maths, 922868, Popular Science, 57, Science & Nature, 1025612, Subjects, 266239, Books, 570896, Non-linear Science, 570874, Applied Mathematics, 564352, Mathematics, 564334, Scientific, Technical & Medical, 1025612, Subjects, 266239, Books, 570936, Geometry, 564352, Mathematics, 564334, Scientific, Technical & Medical, 1025612, Subjects, 266239, Books

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Equivariant, Almost-Arborescent Representations of Open Simply-Connected 3-Manifolds: A Finiteness Result (Memoirs of the American Mathematical Society) - Paperback

ISBN: 0821834606

Taschenbuch, [EAN: 9780821834602], American Mathematical Society, American Mathematical Society, Book, [PU: American Mathematical Society], American Mathematical Society, 56214011, Mathematik, 1320308031, Abbildungen, 56248011, Angewandte Mathematik, 1320307031, Forschung, 56263011, Geometrie & Topologie, 56212011, Geschichte, 56227011, Lernen & Lehren, 56217011, Mathematische Analyse, 56272011, Mathematische Physik, 56218011, Matrizen, 56219011, Messung, 56225011, Nachschlagewerke, 56221011, Populär & Elementar, 56230011, Reine Mathematik, 1320309031, Trigonometrie, 56216011, Unendlichkeit, 56220011, Zahlensysteme, 56047011, Wissenschaft, 54071011, Genres, 52044011, Fremdsprachige Bücher

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Equivariant, Almost-Arborescent Representations of Open Simply-Connected 3-Manifolds (Memoirs of the American Mathematical Society Series #800): A Finiteness Result - Paperback

ISBN: 9780821834602

ID: 9780821834602

Equivariant, Almost-Arborescent Representations of Open Simply-Connected 3-Manifolds (Memoirs of the American Mathematical Society Series #800): A Finiteness Result Equivariant-Almost-Arborescent-Representations-of-Open-Simply-Connected-3-Manifolds~~Valentin-Poenaru Science>Mathematics>Mathematics Paperback, American Mathematical Society

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Equivariant, Almost-Arborescent Representations of Open Simply-Connected 3-Manifolds; A Finiteness Result - Paperback

ISBN: 9780821834602

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Equivariant, Almost-arborescent Representations of Open Simply-connected 3-manifolds - Paperback

2004, ISBN: 9780821834602

ID: 5988067

Softcover, Buch, [PU: American Mathematical Society]

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0821834606

When one extends the (almost) collapsible pseudo-spine representation theorem for homotopy $3$-spheres [Po3] to open simply connected $3$-manifolds $V^3$, new phenomena appear: at the source of the representation, the set of double points is, generally speaking, no longer closed. We show that at the cost of replacing $V^3$ by $V_h^3 = \\{V^3$ with very many holes $\\}$, we can always find representations $X^2 \\stackrel {f} {\\rightarrow} V^3$ with $X^2$ locally finite and almost-arborescent, with $\\Psi (f)=\\Phi (f)$, with the open regular neighbourhood (the only one which is well-defined here) Nbd$(fX^2)=V^3_h$ and such that on any precompact tight transversal to the set of double lines, we have only finitely many limit points (of the set of double points).Moreover, if $V^3$ is the universal covering space of a closed $3$-manifold, $V^3=\\widetilde M^3$, then we can find an $X^2$ with a free $\\pi_1M^3$ action and having the equivariance property $f(gx)=gf(x)$, $g\\in \\pi_1M^3$. Having simultaneously all these properties for $X^2\\stackrel{f} {\\rightarrow} \\widetilde M^3$ is one of the steps in the first author's program for proving that $\\pi_1^\\infty \\widetilde M^3=[UNK]0$, [Po11, Po12]. Achieving equivariance is far from being straightforward, since $X^2$ is gotten starting from a tree of fundamental domains on which $\\pi_1M^3$ cannot, generally speaking, act freely. So, in this paper we have both a representation theorem for general ($\\pi_1=0$) $V^3$'s and a harder equivariant representation theorem for $\\widetilde M^3$ (with $gfX^2=fX^2, \\, g\\in\\pi_1M^3$), the proof of which is not a specialization of the first, 'easier' result.But, finiteness is achieved in both contexts. In a certain sense, this finiteness is a best possible result, since if the set of limit points in question is $\\emptyset$ (i.e. if the set of double points is closed), then $\\pi_1^\\infty V_h^3$ (which is always equal to $\\pi_1^\\infty V^3$) is zero. In [PoTa2] it was also shown that when we insist on representing $V^3$ itself, rather than $V_h^3$, and if $V^3$ is wild ($\\pi_1^\\infty\\not =0$), then the transversal structure of the set of double lines can exhibit chaotic dynamical behavior. Our finiteness theorem avoids chaos at the cost of a lot of redundancy (the same double point $(x, y)$ can be reached in many distinct ways sta

Details of the book - Equivariant, Almost-Arborescent Representations of Open Simply-Connected 3-Manifolds; A Finiteness Result

EAN (ISBN-13): 9780821834602
ISBN (ISBN-10): 0821834606
Paperback
Publishing year: 2004
Publisher: Amer Mathematical Society

Book in our database since 13.02.2008 05:53:48
Book found last time on 18.03.2017 11:48:39
ISBN/EAN: 0821834606

ISBN - alternate spelling:
0-8218-3460-6, 978-0-8218-3460-2

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