Subject: question about the Pontryagin square From: "John R. Klein" Date: Wed, 10 May 2006 05:18:30 -0400 for the list: I am interested in finding out if the Pontryagin square: H^q(X;Z/2) --> H^{2q}(X,Z/4) in the case when X is a closed oriented manifold, has an intepretation as an intersection type invariant on homology, i.e., is there a way of understanding the Poincare dual transformation H_{n-q}(X;Z/2) --> H_{n-2q)(X;Z/4) in terms of representing cycles of the domain as unoriented bordism classes, and performing a geometric operation on these manifold cycles? (Note: if class in the domain admits an itegral lift, then the Pontryagin square is just the self intersection reduced mod 4.) jk John R. Klein, Professor Department of Mathematics Wayne State University Room 1213 FAB, 656 W. Kirby voice: (313) 577-3174 fax: (313) 577-7596