Michael A. Jackson

Associate Professor of Mathematics

These pages are here to give information on my research program. My research is a combination of topology and algebra. In particular it uses areas of algebraic topology including homotopy theory, obstruction theory and cohomology, as well as group theory.

My research program is comprised of several different projects which I will describe below. For preprints and slides from presentations see the preprints page.

One project is concerned with demonstrating free actions of finite groups on finite CW-complexes that are homotopy equivalent to a product of spheres. This work endeavors to prove or disprove a conjecture relating the existence of such actions to the rank of a finite group. To date, I have achieved results for rank two groups as well as rank three p-groups. This project involves obstruction theory, cohomology decompositions of finite groups, as well as the p-fusion of finite groups.

Another project involves finding the strong symmetric genus of finite groups. For a particular finite group, the strong symmetric genus is the smallest genus of a topological surface that the group acts on as a group of orientation preserving automorphisms. I have found the strong symmetric genus of the finite Coxeter groups. This project have been continued by finding the strong symmetric genus of the generalized symmetric groups.

In addition, I am working on research in the area of p-local finite groups. There are several directions this research can take. One direction is to decide which p-groups can have simple fusion systems on them. Another is to classify fusion systems or p-local finite groups on a given p-group.

In addition to my own research I have begun a summer research program for undergraduate students here at Grove City College. For more information see the page on the SOAR program.