Bott and Taubes used integrals over configuration spaces to producefinite-type (a.k.a. Vassiliev) knot invariants. Their techniques were then usedto construct "Vassiliev classes" in the real cohomology spaces of knots andlinks in higher-dimensional Euclidean spaces, using classes in graphcohomology, as first promised by Kontsevich. Here we construct integer-valuedcohomology classes in spaces of knots and links in odd-dimensional Euclideanspaces of dimension greater than three. We construct such a class for anyinteger-valued graph cocycle, by the method of gluing compactifiedconfiguration spaces. Our classes form the integer lattice among the previouslydiscovered real cohomology classes. Thus we obtain nontrivial classes fromtrivalent graph cocycles. We obtain an analogous result modulo 2 when theambient Euclidean space is even-dimensional. Our methods also generalize toconstructing mod-p classes out of mod-p graph cocycles, which need not bereductions of classes over the integers.
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