Arborescent
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Equivariant Almost arborescent Representations of Open Simply connected 3 manifolds
Author | : Valentin Poenaru,C. Tanasi |
Publsiher | : American Mathematical Soc. |
Total Pages | : 89 |
Release | : 2004 |
Genre | : Mathematics |
ISBN | : 9780821834602 |
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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 starting from the singularities).
House documents
Author | : Anonim |
Publsiher | : Unknown |
Total Pages | : 736 |
Release | : 1883 |
Genre | : Electronic Book |
ISBN | : BSB:BSB11547928 |
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Census Reports Tenth Census Report on the forests of North America exclusive of Mexico
Author | : United States. Census Office |
Publsiher | : Unknown |
Total Pages | : 738 |
Release | : 1884 |
Genre | : United States |
ISBN | : CHI:18032821 |
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Report on the Forests of North America exclusive of Mexico
Author | : Charles Sprague Sargent |
Publsiher | : Unknown |
Total Pages | : 680 |
Release | : 1884 |
Genre | : Forests and forestry |
ISBN | : UIUC:30112020119431 |
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Bioinspired Materials Science and Engineering
Author | : Guang Yang,Lin Xiao,Lallepak Lamboni |
Publsiher | : John Wiley & Sons |
Total Pages | : 416 |
Release | : 2018-08-21 |
Genre | : Technology & Engineering |
ISBN | : 9781119390329 |
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An authoritative introduction to the science and engineering of bioinspired materials Bioinspired Materials Science and Engineering offers a comprehensive view of the science and engineering of bioinspired materials and includes a discussion of biofabrication approaches and applications of bioinspired materials as they are fed back to nature in the guise of biomaterials. The authors also review some biological compounds and shows how they can be useful in the engineering of bioinspired materials. With contributions from noted experts in the field, this comprehensive resource considers biofabrication, biomacromolecules, and biomaterials. The authors illustrate the bioinspiration process from materials design and conception to application of bioinspired materials. In addition, the text presents the multidisciplinary aspect of the concept, and contains a typical example of how knowledge is acquired from nature, and how in turn this information contributes to biological sciences, with an accent on biomedical applications. This important resource: Offers an introduction to the science and engineering principles for the development of bioinspired materials Includes a summary of recent developments on biotemplated formation of inorganic materials using natural templates Illustrates the fabrication of 3D-tumor invasion models and their potential application in drug assessments Explores electroactive hydrogels based on natural polymers Contains information on turning mechanical properties of protein hydrogels for biomedical applications Written for chemists, biologists, physicists, and engineers, Bioinspired Materials Science and Engineering contains an indispensible resource for an understanding of bioinspired materials science and engineering.
Forensic Medicine
Author | : P.V. Guharaj |
Publsiher | : Orient Blackswan |
Total Pages | : 490 |
Release | : 2003 |
Genre | : Medical jurisprudence |
ISBN | : 8125024883 |
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This Book Is Written Mainly With The Medical Undergraduate In Mind, But Should Also Prove To Be A Useful Reference For Postgraduate Students And Practitioners. Both The Theory And Practice Of Forensic Medicine And Clinical Toxicology Have Been Given Case Perspectives. Detailed References Have Been Provided At The End Of Each Chapter.
Annals Magazine of Natural History
Author | : Anonim |
Publsiher | : Unknown |
Total Pages | : 494 |
Release | : 1884 |
Genre | : Botany |
ISBN | : PRNC:32101079668859 |
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Geology and Mineralogy as Exhibiting the Power Wisdom and Goodness of God
Author | : William Buckland |
Publsiher | : Unknown |
Total Pages | : 626 |
Release | : 1869 |
Genre | : Bible and geology |
ISBN | : PRNC:32101076808490 |
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