Cobordant manifolds, in the unoriented category of smooth manifolds, are two closed manifolds 
and 
of the same dimension 
whose disjoint
union is diffeomorphic to the entire boundary
of a compact manifold
with boundary 
of dimension 
(Milnor 1965, p. 42; Miller 2021, p. 277). Here
closed means compact and without boundary.
Cobordant Manifold
See also
Bordism, h-Cobordism Theorem, Morse TheoryExplore with Wolfram|Alpha
References
Miller, H. Lectures on Algebraic Topology. Cambridge, MA: Massachusetts Institute of Technology, p. 277, Aug. 27, 2021. https://math.mit.edu/~hrm/papers/lectures-905-906.pdf.Milnor, J. W. Topology from the Differentiable Viewpoint. Charlottesville, VA: University Press of Virginia, p. 42, 1965. https://math.uchicago.edu/~may/REU2017/MilnorDiff.pdf.Referenced on Wolfram|Alpha
Cobordant ManifoldCite this as:
Weisstein, Eric W. "Cobordant Manifold." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/CobordantManifold.html