Subject: Question
Date: Tue, 28 Aug 2001 00:53:15 -0400 (EDT)
From: Adam Sikora <sikora@CRM.UMontreal.CA>
To: Don Davis <dmd1@lehigh.edu>

Dear Prof. Davis,

could you post my question?

I am interested in the following problem:
Given n, find all m such that for any top. space X with
H^1(X)=Z^n, H^2(X,Z)=Z^m
there exist linearly independent v,w in H^1(X,Z) such that v\cup w =0.

In other words, for what n and m, for every skew-symmetric bilinear form
F: Z^n\wedge Z^n -> Z^m there exist linearly independent v,w such that
F(v,w)=0 ?

For example, this statement holds for m<n-1.
(In this situation the kernel of F(v,*): Z^n-> Z^m has dim>1. Hence
there is w in the kernel which is linearly independent from v).
Does the statement hold for bigger m?

Best Regards,
Adam Sikora