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Hempel wrote a book about 3-manifolds in 1976. [5] Personal life. He was married to Edith, whom he married on September 1, 1965, ...
In mathematics, in the topology of 3-manifolds, the loop theorem is a generalization of Dehn's lemma. The loop theorem was first proven by Christos Papakyriakopoulos in 1956, along with Dehn's lemma and the Sphere theorem. A simple and useful version of the loop theorem states that if for some 3-dimensional manifold M with boundary ∂M there ...
If is a prime 3-manifold then either it is or the non-orientable bundle over , or it is irreducible, which means that any embedded 2-sphere bounds a ball. So the theorem can be restated to say that there is a unique connected sum decomposition into irreducible 3-manifolds and fiber bundles of S 2 {\displaystyle S^{2}} over S 1 . {\displaystyle ...
The prime decomposition theorem for 3-manifolds states that every compact, orientable 3-manifold is the connected sum of a unique (up to homeomorphism) collection of prime 3-manifolds. A manifold is prime if it cannot be presented as a connected sum of more than one manifold, none of which is the sphere of the same dimension.
In mathematics, in the topology of 3-manifolds, the sphere theorem of Christos Papakyriakopoulos gives conditions for elements of the second homotopy group of a 3-manifold to be represented by embedded spheres. One example is the following:
Other related books on the mathematics of 3-manifolds include 3-manifolds by John Hempel (1976), Knots, links, braids and 3-manifolds by Victor V. Prasolov and Alexei B. Sosinskiĭ (1997), Algorithmic topology and classification of 3-manifolds by Sergey V. Matveev (2nd ed., 2007), and a collection of unpublished lecture notes on 3-manifolds by Allen Hatcher.
Young’s shooting has dipped to 40% and his 3-point shooting is at 34%. Those numbers are well below his career marks and his field-goal shooting is a career worst. The advanced stats aren’t ...
A paper of Kobayashi (2001) classifies the Heegaard splittings of hyperbolic three-manifolds which are two-bridge knot complements. Computational methods can be used to determine or approximate the Heegaard genus of a 3-manifold. John Berge's software Heegaard studies Heegaard splittings generated by the fundamental group of a manifold.