Recall that a closed manifold is compact with no boundary. Stokes' Theorem tells us that it is important to ask whether a closed manifold bounds a larger one. Bordism is a tool which tests a topological space X by considering which maps of closed manifolds into X are restrictions from manifolds with boundaries. Complex bordism, because of its power and convenience (its coefficients form an integral polynomial ring), has become a classic tool for topologists. It has had applications to stable homotopy and to immersion theory: it even has connection with the elliptic homology of Ochanine. Localized at a prime p, complex bordism is determined by Brown-Peterson homology. My interests have been concerned with computation in Brown-Peterson homology and with unstable operations in the theory.
Some recent publications:
- (With W. Stephen Wilson and Dung Yung Yan) Brown-Peterson homology of elementary p-groups II, Topology and its Applications 59 (1994), 117--136
- (With J. Michael Boardman and W. Stephen Wilson) Unstable operations in generalized cohomology, Handbook of Algebraic Topology, I. M. James, ed., Amsterdam: Elsevier Science (1995), 687-828
- (With George Nakos) The Brown-Peterson 2k-series revisited, Journal of Pure and Applied Algebra (to appear)