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Almost mathematicians wish to study on the classification of the objects within isomorphism and determination of effective and computable invariants to distinguish the isomorphism classes. In topology, the concepts of homotopy and homeomorphism are such examples. In this lecture I shall speak of with respect to (i) Thom's cobordism group (ii) Cobordism category (iii) finally, the semigroup in cobordism category is isomorphic to the Thom's cobordism group.

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