Assembly Map
In mathematics, assembly maps are an important concept in geometric topology. From the homotopy-theoretical viewpoint, an assembly map is a universal approximation of a homotopy invariant functor by a homology theory from the left. From the geometric viewpoint, assembly maps correspond to 'assemble' local data over a parameter space together to get global data.
Assembly maps for algebraic K-theory and L-theory play a central role in the topology of high-dimensional manifolds, since their homotopy fibers have a direct geometric interpretation. Equivariant assembly maps are used to formulate the Farrell–Jones conjectures in K- and L-theory.
Read more about Assembly Map: Homotopy-theoretical Viewpoint, Geometric Viewpoint, Importance in Geometric Topology
Famous quotes containing the words assembly and/or map:
“Our assembly being now formed not by ourselves but by the goodwill and sprightly imagination of our readers, we have nothing to do but to draw up the curtain ... and to discover our chief personage on the stage.”
—Sarah Fielding (1710–1768)
“Unless, governor, teacher inspector, visitor,
This map becomes their window and these windows
That open on their lives like crouching tombs
Break, O break open,”
—Stephen Spender (1909–1995)