Reg Wood's Home Page

Reg Wood
Mathematics Department
Manchester University
Oxford Road
Manchester
M13 9PL
England

reg@ma.man.ac.uk

0161 275 5849

page1 for recent preprints
page2 for recent publications
page3 for older publications
page4 for problems

Research Interests

In recent years my interests have been in a branch of topology concerned mainly with the action of the Steenrod algebra A on polynomials. From the topological point of view A is the algebra of universal stable operations in ordinary cohomology theory and has been of fundamental importance in the development of algebraic topology since the first publication on the subject by Steenrod in 1947. The action of A on polynomials arises from the cohomology of certain particular spaces, namely products of infinite projective spaces. However, these examples are in a sense universal and determine the algebra itself. They also provide the launching pad for a purely algebraic development of the Steenrod algebra, which has led to many interconnections with such subjects as modular representation theory of matrix semigroups, invariant theory, differential operators and the combinatorics of symmetric functions, see Problems in the Steenrod algebra . There are many unsolved problems concerned both with the internal structure of A as well as its action on polynomials. Many of these questions go under the umbrella title of `hit problems' and are concerned with the general question in algebra of finding minimal generating sets for modules over rings, see Ioannina article .

From time to time I have taken an interest in a number of other subjects, usually with some connection to algebraic topology, for example, Bott periodicity, homotopy groups of spheres and framed bordism, embedding Lie groups in euclidean space, polynomial maps of affine varieties, quaternionic eigenvalues, Julia sets, the 3x+1 problem. On page 4 problems there is a miscellaneous collection of questions, gathered over the years, which may intrigue the reader.

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