  We define and study the notion of numerical equivalence on algebraic
cobordism cycles. We prove that algebraic cobordism modulo numerical
equivalence is a finitely generated module over the Lazard ring, and it
reproduces the Chow group modulo numerical equivalence. We show this theory
defines an oriented Borel-Moore homology theory on schemes and oriented
cohomology theory on smooth varieties.
  We compare it with homological equivalence and smash-equivalence for
cobordism cycles. For the former, we show that homological equivalence on
algebraic cobordism is strictly finer than numerical equivalence, answering
negatively the integral cobordism analogue of the standard conjecture $(D)$.
For the latter, using Kimura finiteness on cobordism motives, we partially
resolve the cobordism analogue of a conjecture by Voevodsky on rational
smash-equivalence and numerical equivalence.
