Given a finite, connected 2-complex $X$ such that $b_2(X)le1$ we establishtwo existence results for representations of the fundamental group of $X$ intocompact connected Lie groups $G$, with prescribed values on certain loops. If$b_2(X)=1$ we assume $G=SO(3)$ and that the cup product on the first rationalcohomology group of $X$ is non-zero.
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机译:给定有限,连接的2个复杂$ x $,即$ b_2(x) le1 $ we,我们建立了$ x $ Intocompact连接Lie Groups $ G $的基本组的表现的结果,在某些环路上具有规定的值。如果$ b_2(x)= 1 $我们假设$ g = so(3)$,并且第一个理性的x $的杯子产品是非零的。
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