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