A topological resolution theorem
We construct an explicit categorification of the action of tangles on tensor powers of the fundamental representation of quantum sl(2).
In questo articolo studiamo i gruppi di una sfera e proviamo che il gruppo è isomorfo all'ennesimo gruppo di omotopia di , nell'ipotesi che sia una classe coconnessa di links ammissibili.
In this note we give examples in every dimension of piecewise linearly homeomorphic, closed, connected, smooth -manifolds which admit two smoothness structures with differing spans, stable spans, and immersion co-dimensions. In dimension the examples include the total spaces of certain -sphere bundles over . The construction of such manifolds is based on the topological variance of the second Pontrjagin class: a fact which goes back to Milnor and which was used by Roitberg to give examples...
We classify the genus one compact (PL) 5-manifolds and prove some results about closed 5-manifolds with free fundamental group. In particular, let be a closed connected orientable smooth -manifold with free fundamental group. Then we prove that the number of distinct smooth -manifolds homotopy equivalent to equals the -nd Betti number (mod ) of .