Paths and cylinders
For a vector space or -module, a quadratic form on is a function
such that for all ,
and the polarization of
is a bilinear form.
be a bilinear form. We say a function is a quadratic refinement of if
for all .
If this exists, then
So a quadratic refinement always exists when is invertible. Otherwise its existence is a non-trivial condition.
Course notes include for instance
Quadratic refinements of intersection pairing in cohomology is a powerful tool in algebraic topology and differential topology. See
Revised on October 13, 2013 02:56:41
by Urs Schreiber