R. E. Stong

Circle actions on spin manifolds and characteristic numbers

II+ 1970 Atiyah and Hirzebruch [3] proved that the existence of a non-trivial smooth action of the circle group S’ on a closed connected Spin manifold M implies that the A-genus of M vanishes. It is our purpose to explore the vanishing of further Pontrjagin numbers of Spin manifolds admitting smooth S’ actions of odd type; assuming that MS’ # 4, and viewing Z, = ( k 1) c S’, these are the actions for which all components of the fixed set MzL have codimensions congruent to 2 (mod 4) (see [2,3]). We have one general result for such actions; the rest of our results require that the action also be semifree, i.e. that it be free on the complement of the fixed set MS’. The following result was proved during conversations with S. Weinberger.

Invariants of binary bilinear forms modulo two

In this note we examine the invariant theory of binary bilinear forms over the field F 2 of two elements that arises in the classification of standardly graded Poincare duality algebras with two generators over the field F 2 of two elements. We compute the corresponding ring of invariants and find separating invariants for the orbit space.

Thom modules and pseudoreflection groups

Abstract This paper studies the structure of Thom modules. These are the purely algebraic analogue of the cohomology of a Thom space. Special emphasis is placed on Thom modules over the ring of invariants of a finite group generated by pseudoreflections.

A bilinear form for Spin manifolds

On etudie la forme bilineaire sur H j (M;Z 2 ) definie par [x,y]=xSq 2 y[M] quand M est une variete spin fermee de dimension 2j+2

Cohomology of a bounding manifold

This paper characterizes those subsets of H*(M; Q) which are the image of the cohomology of some manifold whose boundary is M.