Novikov additivity I (Ex)
From Manifold Atlas
Revision as of 10:09, 29 May 2012 by Tibor Macko (Talk | contribs)
Let be a -dimensional manifold with boundary, . Consider the homomorphism and denote the image of . Coefficients are understood to be in .
The middle dimensional intersection form
is degenerate in general. Show that the intersection form on defined by
is a non-degenerate symmetric bilinear form and let us define the signature to be the signature of this form.
Suppose that we have also another -dimensional manifold with boundary . Form the closed manifold . Show that
Observe that the analogous statement is true if we replace manifols with boundary by Poincare pairs.
Hint: section 7 of ASIT III