higher geometry / derived geometry
geometric little (∞,1)-toposes
geometric big (∞,1)-toposes
function algebras on ∞-stacks?
derived smooth geometry
(see also Chern-Weil theory, parameterized homotopy theory)
vector bundle, (∞,1)-vector bundle
topological vector bundle, differentiable vector bundle, algebraic vector bundle
direct sum of vector bundles, tensor product of vector bundles, inner product of vector bundles?, dual vector bundle
A “branched” or “ramified” covering spaces is much like a plain covering space, only that over isolated points in the base space – called the branch point or ramification points – sheets of the covering may merge.
The archetypical examples in complex analysis and here the most archetypical example of all is the graph of (any choice of) the square root function on the complex plane, which is a double cover away from the point at the origin, but including the origin it is a branched double cover with branch point that origin
Dually branching is reflected in rings of functions by ramification of ideals.
Notably under the function field analogy one may also understand ramification of ideals in number fields as encoding branched coverings (“over Spec(F1)”)
Wikipedia, Branched covering
Jürgen Neukirch, Algebraische Zahlentheorie (1992), English translation Algebraic Number Theory, Grundlehren der Mathematischen Wissenschaften 322, 1999 (pdf)
Last revised on July 23, 2014 at 06:43:48. See the history of this page for a list of all contributions to it.