Abstract:
A study is made of the integral over $l$-dimensional sphere $\overline\Sigma$ of a meromorphic differential form that has poles on $m$ hyperplanes $\overline P_j$. This integral is a many-valued analytic function with discontinuities across the Landau variety $L$. A study is made of the discontinuities of the integral across $L$ and also the representation of $\pi_1(C^{m(l+1)}-L)$ on the homology group $H_{l^c}(\overline{\Sigma}-\displaystyle\bigcup_{j=1}^m(\overline{\Sigma}\bigcap\overline{P_j}))$ for the case $m=l+1, l+2$.
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