We have two main results. 1. Let P : Kn → Kn be a polynomial map with constant nonzero Jacobian, where K is any extension of Q. Then, P has a polynomial inverse if and only if the range of P contains a cartesian product of n universal Hilbert sets. 2. Let P : K → K be a polynomial map with constant nonzero Jacobian, where K is an algebraic number field. Then, P is invertible for “almost all” ra...

Abstract. We show that the Strong Novikov Conjecture for the maximal C∗-algebra C∗(π) of a discrete group π is equivalent to a statement in topological K-theory for which the corresponding statement in algebraic K-theory is always true. We also show that for any group π , rational injectivity of the full assembly map for K ∗(C ∗(π)) follows from rational injectivity of the restricted assembly map.

We give an overview of results on the second Gaussian map for curves in relation to the second fundamental form of the period map. We will also concentrate on the case in which the curve is contained in an abelian surface, or in a K3 surface. This is an expanded version of the talk given at the “Workshop on Hodge Theory and Algebraic Geometry” in Povo (Trento) on 4–5 September 2009.

C. OGLE Department of Mathematics, Ohio State University, Columbus, 0H43210, U.S.A. (Received: March 1992) Abstraet. Following Connes and Moscovici, we show that the Baum-Connes assembly map for K,(C~*n) is rationally injective when n is word-hyperbolic, implying the Equivariant Novikov conjecture for such groups. Using this result in topological K-theory and BoreI-Karoubi regulators, we also s...

With the recent developments in the C++ language, concepts are mostly discussed as a form of constrained polymorphism. Yet, concepts also allow for an alternative, implementation-independent view that comes from their origin in (algebraic) specification languages. In this paper, we return to this specification view on concepts and formalize C++ concepts as institutions, a well-established notio...

It is known that isomorphisms of graph Jacobians induce cyclic bijections on the associated graphs. We characterize when such can be strengthened to isomorphisms, in terms an easily computed divisor. The result refines tools used algebraic geometry examine fibers compactified Torelli map.