higher geometry / derived geometry
Ingredients
Concepts
geometric little (∞,1)-toposes
geometric big (∞,1)-toposes
Constructions
Examples
derived smooth geometry
Theorems
homotopy theory, (∞,1)-category theory, homotopy type theory
flavors: stable, equivariant, rational, p-adic, proper, geometric, cohesive, directed…
models: topological, simplicial, localic, …
see also algebraic topology
Introductions
Definitions
Paths and cylinders
Homotopy groups
Basic facts
Theorems
By a hyperplane one usually means an affine or linear subspace of an affine space or linear space, respectively, typically required to be a positive dimension and codimension and often required to have codimension = 1.
In the archetypical example the ambient space is the time-honored Euclidean/Cartesian space and a hyperplane of codimension 1 is an ordinary plane.
More sophisticated examples arise for instance in the discussion of configuration spaces of points in a Cartesian space , where hyperplanes in given by reflect the subspaces where positions of a given pair of points coincide. This leads to discussion of arrangements of hyperplanes and their complements, see also at Knizhnik-Zamolodchikov equation the references on twisted cohomology of configuration spaces of points.
See also:
Created on July 14, 2022 at 11:28:09. See the history of this page for a list of all contributions to it.