Don't know if this contains what you're thinking of, Fred, but it certainly is a fascinating survey of quadratic forms over the integers, showing just how nontrivial this subject is: https://math.nd.edu/assets/20630/hahntoulouse.pdf <https://math.nd.edu/assets/20630/hahntoulouse.pdf>. The theory of quadratic forms over the integers is central to the theory of topological 4-manifolds, because of Michael Freedman's 1982 theorem (here cribbed from notes on the web): ----- Theorem 1. For each symmetric bilinear unimodular form Q over Z there exists a closed oriented simply-connected topological 4-manifold with Q as its intersection form. If Q is even there is precisely one; if Q is odd there are precisely two, at least one of which is nonsmoothable. ----- —Dan
On Jan 30, 2016, at 8:57 AM, Fred Lunnon <fred.lunnon@gmail.com> wrote:
I have been struggling to recall a rather surprising theorem, encountered in passing while searching for something unrelated, concerning the structure of quadratic spaces for which the Witt index exceeds 2 . Not only can I not find the theorem; I can't even locate a definition of the Witt index --- that is |p - q| + r , where the (possibly degenerate) quadratic form signature involves p positive, q negative, r absent squares.
Can somebody out there please unscramble my brain (or my surfing technique) for me? Dribble, mutter ...