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
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Let
be a bilinear form. A (quadratic) function
is called a quadratic refinement of if
for all .
If such is indeed a quadratic form in that then and
This means that a quadratic refinement by a quadratic form always exists when is invertible. Otherwise its existence is a non-trivial condition. One way to express quadratic refinements is by characteristic elements of a bilinear form. See there for more.
Quadratic refinements of intersection pairing in cohomology is a powerful tool in algebraic topology and differential topology. See:
Last revised on May 7, 2022 at 19:59:52. See the history of this page for a list of all contributions to it.