Novikov additivity I (Ex)
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\textup{Sign} (Z) = \textup{Sign} (Y') + \textup{Sign} (Y). | \textup{Sign} (Z) = \textup{Sign} (Y') + \textup{Sign} (Y). | ||
$$ | $$ | ||
+ | |||
+ | Observe that the analogous statement is true if we replace manifols with boundary by Poincare pairs. | ||
+ | |||
Hint: section 7 of ASIT III | Hint: section 7 of ASIT III | ||
</wikitex> | </wikitex> |
Revision as of 10:09, 29 May 2012
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