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topsigns.tex,v
head 1.1; access; symbols; locks; strict; comment @% @; 1.1 date 2007.10.13.16.01.42; author mellit; state Exp; branches; next ; desc @@ 1.1 log @first addition @ text @\input commons.tex \begin{document} \section{Signs of topological operations} The dual of a cohomology class $x$ is $x\cap o$. If $y$ is a complementary cohomology class then \[ (x\cap o)\bullet(y\cap o) = (x\cup y) \cap o, \qquad\text{page 337 in Dold.} \] Applying p.239 \[ \langle 1, (x\cup y) \cap o\rangle = \langle x\cup y, o\rangle = \langle x, y\cap o\rangle. \] So for any cohomology class $x$ and cohomology class $\xi$ \[ \langle x, \xi\rangle = (x\cap o) \bullet \xi. \] \end{document}@
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