Our main result expresses certain algebraic invariants
of B in terms of the cohomology of simplicial complexes associated with its R-poset.
Chapter 9 begins with a survey of Jules Vuillemin's approach to the philosophy of mathematics and then proceeds to examine De Rham's theorem, which, by employing multiple modes of representation, demonstrates an isomorphism between two sets of algebraic invariants
associated with a smoothly triangulated manifold.
This discovery led to the formulation of a host of new algebraic invariants
(or knot polynomials), computed from knot diagrams, that distinguish among knots more effectively than earlier schemes (SN: 10/26/85, p.
The first major step in classifying four-manifolds was a proof that certain types could be identified on the basis of algebraic invariants
called quadratic forms.