The Poincaré homology sphere and almost-simple knots in lens spaces
نویسندگان
چکیده
منابع مشابه
And Knots in Lens Spaces
We determine the non-null homologous knots in lens spaces whose exteriors contain properly embedded once-punctured tori. All such knots arise as surgeries on the Whitehead link and are grid number 1 in their lens spaces. As a corollary, we classify once-punctured torus bundles that admit a lens space filling.
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For a closed 4-manifold X and closed 3-manifold M we investigate the smallest integer n (perhaps n = ∞) such that M embeds in #nX , the connected sum of n copies of X. It is proven that any lens space (or homology lens space) embeds topologically locally flatly in #2(CP # CP 2 ), in #4S 2 × S and in #8CP .
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A homology lens space is a closed 3-manifold with Z-homology groups isomorphic to those of a lens space. A useful theorem found in [Fu] states that a homology lens space M3 may be obtained by an (n/1)-Dehn surgery on a homology 3-sphere if and only if the linking form of M3 is equivalent to (1/n). In this note we generalize this result to cover all homology lens spaces, and in the process offer...
متن کاملOn the homology of the spaces of long knots
Keywords: discriminant of the space of knots, bialgebra of chord diagrams, Hochschild complex, operads of Poisson – Gerstenhaber – Batalin-Vilkovisky algebras. This paper is a more detailed version of [T1], where the first term of the Vassiliev spectral sequence (computing the homology of the space of long knots in R d , d ≥ 3) was described in terms of the Hochschild homology of the Poisson al...
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Henri Poincaré formulated the mathematics of Lorentz transformations, known as the Poincaré group. He also formulated the Poincaré sphere for polarization optics. It is shown that these two mathematical instruments can be derived from the two-by-two representations of the Lorentz group. Wigner’s little groups for internal space-time symmetries are studied in detail. While the particle mass is a...
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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 2013
ISSN: 0002-9939,1088-6826
DOI: 10.1090/s0002-9939-2013-11832-0