With no explanation, label text_A→text_B with either "not_related" or "related".
text_A: David Bowie starred in The Shining.
text_B: In mathematics , cobordism is a fundamental equivalence relation on the class of compact manifolds of the same dimension , set up using the concept of the boundary -LRB- French bord #French , giving cobordism -RRB- of a manifold .. mathematics. mathematics. equivalence relation. equivalence relation. compact. compact space. manifold. manifold. boundary. boundary ( topology ). Two manifolds of the same dimension are cobordant if their disjoint union is the boundary of a compact manifold one dimension higher .. compact. compact space. manifold. manifold. boundary. boundary ( topology ). disjoint union. disjoint union. The boundary of an -LRB- n + 1 -RRB- - dimensional manifold W is an n-dimensional manifold ∂ W that is closed , i.e. , with empty boundary .. manifold. manifold. boundary. boundary ( topology ). In general , a closed manifold need not be a boundary  : cobordism theory is the study of the difference between all closed manifolds and those that are boundaries .. manifold. manifold. boundary. boundary ( topology ). The theory was originally developed for smooth manifolds -LRB- i.e. , differentiable -RRB- , but there are now also versions for piecewise-linear and topological manifolds .. piecewise-linear and topological manifolds. #Cobordism of piecewise linear and topological manifolds. A cobordism between manifolds M and N is a compact manifold W whose boundary is the disjoint union of M and N , .. compact. compact space. manifold. manifold. boundary. boundary ( topology ). disjoint union. disjoint union. Cobordisms are studied both for the equivalence relation that they generate , and as objects in their own right .. equivalence relation. equivalence relation. Cobordism is a much coarser equivalence relation than diffeomorphism or homeomorphism of manifolds , and is significantly easier to study and compute .. equivalence relation. equivalence relation. diffeomorphism. diffeomorphism. homeomorphism. homeomorphism. It is not possible to classify manifolds up to diffeomorphism or homeomorphism in dimensions ≥ 4 -- because the word problem for groups can not be solved -- but it is possible to classify manifolds up to cobordism .. diffeomorphism. diffeomorphism. homeomorphism. homeomorphism. word problem for groups. word problem for groups. Cobordisms are central objects of study in geometric topology and algebraic topology .. geometric topology. geometric topology. algebraic topology. algebraic topology. In geometric topology , cobordisms are intimately connected with Morse theory , and h-cobordisms are fundamental in the study of high-dimensional manifolds , namely surgery theory .. geometric topology. geometric topology. intimately connected. #Connection with Morse theory. Morse theory. Morse theory. surgery theory. surgery theory. In algebraic topology , cobordism theories are fundamental extraordinary cohomology theories , and categories of cobordisms are the domains of topological quantum field theories .. algebraic topology. algebraic topology. extraordinary cohomology theories. extraordinary cohomology theories. categories of cobordisms. #Categories of cobordisms. topological quantum field theories. topological quantum field theory
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