We give a geometric setup in which the connecting homomorphism in the localization long exact sequence for Witt groups decomposes as the pullback to the exceptional fiber of a suitable blow-up followed by a push-forward.

If g(t) is a three-dimensional Ricci flow solution, with sectional curvatures that are O(t) and diameter that is O(t 1 2 ), then the pullback Ricci flow solution on the universal cover approaches a homogeneous expanding soliton.

Graph rewriting has numerous applications, such as software engineering and biology techniques. This technique is theoretically based on pushouts and pullbacks, which are involved with given categories. This paper deals with the definition of pushout and pullback, and their properties.

Converse Lyapunov theorems are presented for nonautonomous systems modelled as skew product flows. These characterize various types of stability of invariant sets and pullback, forward and uniform attractors in such nonautonomous systems. MSC subject classification: 37B25, 37B55, 93D30

Principal comodule algebras can be thought of as objects representing principal bundles in non-commutative geometry. A crucial component of a principal comodule algebra is a strong connection map. For some applications it suffices to prove that such a map exists, but for others, such as computing the associated bundle projectors or Chern–Galois characters, an explicit formula for a strong conne...