Danny Ruberman
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Registered User
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May 8 |
answered | The classifying space of a gauge group |
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May 8 |
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Classification of higher dimensional manifolds In that case, a topological classification for highly-connected 2n-manifolds with given intersection form with n even should be straightforward from the surgery exact sequence and the computation of the homotopy groups of G/TOP. Kreck's paper gives a good guide, or you could try Ranicki chapter 13 (eg example 13.26 for a sense of what the answer would look like). For existence of manifolds with given intersection form, look at the last chapter (plumbing) of Browder's book, Surgery on simply-connected manifolds. |
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May 7 |
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Classification of higher dimensional manifolds A more careful answer to the original question would be that there is not really going to be a good classification, especially when n is even, as Allen remarks. That's because the simplest homotopy invariant is the intersection form, and symmetric unimodular forms still defy classification; cf. Milnor-Husemoller's book on the subject. Perhaps Allen could clarify his question, which asks about classification up to homeomorphism; this is probably realistic (or maybe easy) for fixed intersection form. But up to diffeomorphism it's a more complicated story. |
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May 6 |
answered | Classification of higher dimensional manifolds |
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May 2 |
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Does a *topological* manifold have an exhaustion by compact submanifolds with boundary? Here's an easier (in the sense of quoting fewer results) argument in dimension 4. There is nothing to prove for compact manifolds. In the same paper (Ends of Maps III: Dimensions 3 and 4, JDG 17 (1982)) in which he proved the existence of handle structures and gave transversality results, Quinn proved that non-compact 4-manifolds are smoothable. Hence your favorite method for smooth manifolds will work. In real terms, this isn't any easier, since this argument and the one Ricardo gives depend on essentially the same set of ideas. |
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Apr 4 |
accepted | Linkage between singularities of algebraic varieties and continued fractions |
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Apr 4 |
answered | Linkage between singularities of algebraic varieties and continued fractions |
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Feb 20 |
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How to see the quaternionic hopf map generates the stable 3-stem? Chris: Ryan's argument isn't circular. Starting with a Heegaard splitting of M (from a triangulation or Morse function), you get M as surgery on a link. This already shows $\Omega_3$ is trivial. An algorithm of S. Kaplan encodes a spin structure on M in terms of a "characteristic sublink" of this link, and shows how to find a bounding spin manifold by eliminating the characteristic sublink. This route seems easier to me than the AHSS, but as you say this depends on one's perspective. |
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Feb 6 |
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Trichotomies in mathematics A connected sum is a satellite knot, albeit in a somewhat trivial way, cf. en.wikipedia.org/wiki/Satellite_knot. So there's no need to restrict to prime knots for this trichotomy to work. |
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Jan 24 |
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proper use of the word “stereographic” I've got to agree with Lee; after all, nobody seems to worry too much about the use of the word `volume' to describe measure in n dimensions for $n>3$. |
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Dec 1 |
answered | Lefschetz duality for twist coefficient |
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Nov 26 |
answered | Topology of the Universal Spinor Field Bundle |
