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Geometric models of twisted differential K-theory I
This is the first in a series of papers constructing geometric models of twisted differential K-theory. In this paper we construct a model of even twisted differential K-theory when the underlying topological twist represents a torsion class. By differential twists we will mean smooth U(1)-gerbes with connection, and we use twisted vector bundles with connection as cocycles. The model we construct satisfies the axioms of Kahle and Valentino, including functoriality, naturality of twists, and the hexagon diagram. This paper confirms a long-standing hypothetical idea that twisted vector bundles with connection define twisted differential K-theory
Homologous Non-isotopic Symplectic Tori in Homotopy Rational Elliptic Surfaces
Let E(1)_K denote the closed 4-manifold that is homotopy equivalent (hence
homeomorphic) to the rational elliptic surface E(1) and is obtained by
performing Fintushel-Stern knot surgery on E(1) using a knot K in S^3. We
construct an infinite family of homologous non-isotopic symplectic tori
representing a primitive homology class in E(1)_K when K is any nontrivial
fibred knot in S^3. We also show how these tori can be non-isotopically
embedded as homologous symplectic submanifolds in other symplectic 4-manifolds.Comment: 8 pages, 2 figure
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