Abstract

This written work, by Benedetta Andina, discusses ``The cobordism ring: the prospective of characteristic classes''. After providing sufficient preliminaries to make this thesis accessible to any graduate student, it clearly highlights how both the oriented and unoriented cobordism rings can be studied using characteristic classes, which are usually easily computable. To demonstrate this relationship in the unoriented case (as presented by Pontrjagin and Thom), the author unveils an explicit structure of the unoriented cobordism ring. This structure provides a clear classification of smooth closed manifolds.