  We define a cobordism theory in algebraic geometry based on normal crossing
degenerations with double point singularities. The main result is the
equivalence of double point cobordism to the theory of algebraic cobordism
previously defined by Levine and Morel. Double point cobordism provides a
simple, geometric presentation of algebraic cobordism theory. As a corollary,
the Lazard ring given by products of projective spaces rationally generates all
nonsingular projective varieties modulo double point degenerations. Double
point degenerations arise naturally in relative Donaldson-Thomas theory. We use
double point cobordism to prove all the degree 0 conjectures in
Donaldson-Thomas theory: absolute, relative, and equivariant.
