Preface xv

I would like to acknowledge the partial support of NSF Grant DMS 05-

55776. Gunnells was supported in part by NSF Grants DMS 02-45580 and

DMS 04-01525.

Notation and Conventions. We denote canonical isomorphisms by

∼

=

and noncanonical isomorphisms by ≈. If V is a vector space and s denotes

some sort of construction involving V , we let Vs denote the corresponding

subspace and V

s

the quotient space. E.g., if ι is an involution of V , then

V+ is Ker(ι − 1) and V

+

= V/Im(ι − 1). If A is a finite abelian group, then

Ator denotes the torsion subgroup and A/tor denotes the quotient A/Ator.

We denote right group actions using exponential notation. Everywhere in

this book, N is a positive integer and k is an integer.

If N is an integer, a divisor t of N is a positive integer such that N/t is

an integer.