Dimensional Reduction of Cobordism and K-theory

Spin Cobordism Determines Real K-theory

Cobordism Theory Using Steenrod Operations

In this paper I give new proofs of the structure theorems for the unoriented cobordism ring [12] and the complex cobordism ring [8, 131. The proofs are elementary in the sense that no mention of the Steenrod algebra or Adams spectral sequence is made. In fact, the only result from homotopy theory which is used in an essential way is the Serre finiteness theorem in order to know that the complex...

An Introduction to Cobordism Theory

The notion of cobordism is simple; two manifolds M and N are said to be cobordant if their disjoint union is the boundary of some other manifold. Given the extreme difficulty of the classification of manifolds it would seem very unlikely that much progress could be made in classifying manifolds up to cobordism. However, René Thom, in his remarkable, if unreadable, 1954 paper Quelques propriétés...

The Cobordism of Oriented Three Dimensional Orbifolds

In a previous paper [2], using orbifold Pontrjagin numbers, we had established that rationally every odd dimensional oriented orbifold bounds and, also, if an orbifold bounds, then some multiple of it bounds with no increase in the set of local groups. The proof involves systematically making the orbifold rationally cobordant to one with a smaller set of local groups. Thus to study torsion in o...

The Impact of Thom’s Cobordism Theory

At the 1958 International Congress of Mathematicians in Edinburgh, René Thom received one of two Field Medals for his development of cobordism. In his citation [11] Heinz Hopf described the definition of cobordism as one of those elementary and apparently trivial constructions which can hardly be expected to yield significant results. He compares this with Hurewicz’s definition of homotopy grou...