FINITE LOCALITIES I
Andrew Chermak
Kansas State University June 2020
This is the first of (at present) two papers concerning what might be
thought of as “locally grouped spaces”, in loose analogy with the
locally ringed spaces of algebraic geometry. The spaces that we have
in mind are simplicial sets that generalize the simpli- cial sets that
underly and determine the classifying spaces of finite (or compact)
groups. If the analogy is pursued, then the role of “structure sheaf”
is provided by the “fu- sion systems” associated with these spaces.
Our approach here will be purely algebraic and combinatorial, so we
will not be concerned with topological realizations. All of the groups
to be considered will be finite; but a parallel series of papers,
co-authored with Alex Gonzalez, will considerably broaden the scope.