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
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
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