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Mazur manifold information


In differential topology, a branch of mathematics, a Mazur manifold is a contractible, compact, smooth four-dimensional manifold-with-boundary which is not diffeomorphic to the standard 4-ball. Usually these manifolds are further required to have a handle decomposition with a single -handle, and a single -handle; otherwise, they would simply be called contractible manifolds. The boundary of a Mazur manifold is necessarily a homology 3-sphere.

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Mazur manifold

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topology, a branch of mathematics, a Mazur manifold is a contractible, compact, smooth four-dimensional manifold-with-boundary which is not diffeomorphic...

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Barry Mazur

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in number theory, Mazur's torsion theorem in arithmetic geometry, the Mazur swindle in geometric topology, and the Mazur manifold in differential topology...

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Isometry

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the manifold; a manifold with a (positive-definite) metric is a Riemannian manifold, one with an indefinite metric is a pseudo-Riemannian manifold. Thus...

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Schoenflies problem

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n-ball? For n = 4, the problem is still open for both categories. See Mazur manifold. For n ≥ 5 the question in the smooth category has an affirmative answer...

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Geometric topology

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Mazur received the Veblen Prize for their independent proofs of this theorem. Low-dimensional topology includes: Surfaces (2-manifolds) 3-manifolds 4-manifolds...

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Wild knot

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their decorative purposes in Celtic-style ornamental knotwork. Eilenberg–Mazur swindle, a technique for analyzing connected sums using infinite sums of...

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Arithmetic topology

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Barry Mazur, c.1964 B. Mazur, Notes on ´etale cohomology of number fields, Ann. scient. ´Ec. Norm. Sup. 6 (1973), 521-552. A. Reznikov, Three-manifolds class...

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List of things named after Stefan Banach

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Banach manifold Banach measure Banach space Banach coordinate space Banach disks Banach norm Banach–Alaoglu theorem Banach–Mazur compactum Banach–Mazur game...

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Analytic torsion

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topology; see (Mazur). For more recent work on torsion see the books (Turaev 2002) and (Nicolaescu 2002, 2003). If M is a Riemannian manifold and E a vector...

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Algebraic topology

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smooth manifolds via de Rham cohomology, or Čech or sheaf cohomology to investigate the solvability of differential equations defined on the manifold in question...

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Local flatness

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imbeddings [sic] of topological manifolds. Annals of Mathematics, Second series, Vol. 75 (1962), pp. 331–341. Mazur, Barry. On embeddings of spheres...

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Stefan Banach

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paradox, the Hahn–Banach theorem, the Banach–Steinhaus theorem, the Banach–Mazur game, the Banach–Alaoglu theorem, and the Banach fixed-point theorem. Stefan...

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Morris Hirsch

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Barry Mazur: Smoothings of piecewise linear manifolds, Princeton University Press 1974 with Charles C. Pugh, Michael Shub: Invariant Manifolds, Springer...

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Oswald Veblen Prize in Geometry

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Brown and Barry Mazur 1971 Robion Kirby 1971 Dennis Sullivan 1976 William Thurston 1976 James Harris Simons 1981 Mikhail Gromov for: Manifolds of negative...

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Michael Artin

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cohomology, jointly with Alexander Grothendieck. He also collaborated with Barry Mazur to define étale homotopy theory which has become an important tool in algebraic...

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Connected sum

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of connected sum is a geometric modification on manifolds. Its effect is to join two given manifolds together near a chosen point on each. This construction...

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Periodic table

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Within 100 years of the appearance of Mendeleev's table in 1869, Edward G. Mazurs had collected an estimated 700 different published versions of the periodic...

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List of general topology topics

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(topology) Ultrafilter Baire category theorem Nowhere dense Baire space Banach–Mazur game Meagre set Comeagre set Compact space Relatively compact subspace Heine–Borel...

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List of theorems

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theorem (combinatorics) Banach–Alaoglu theorem (functional analysis) Banach–Mazur theorem (functional analysis) Banach fixed-point theorem (metric spaces...

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