Abstract:

According to folklore, it is impossible to construct a faithful finite dimensional algebraic model of differential forms
which preserves all three properties of (graded) commutativity, associativity and the Leibniz rule.
In this talk we will demonstrate how by enlarging a cubical complex by adding certain "ideal" elements,
a combinatorial transverse intersection algebra model of a torus can be constructed which does have
graded commutativity and associativity while the product rule holds for elements of the original complex.
One application of this algebra is to create a finite dimensional fluid algebra which can be implemented
numerically for approximation to Euler's equation on a torus.
This is joint work with Daniel An and Dennis Sullivan.