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Later Atiyah and Singer showed that index theorems for elliptic operators on closed manifolds with infinite fundamental group could naturally be phrased in terms of unbounded operators affiliated with the von Neumann algebra of the group.
If one considers the control flow graph as a 1-dimensional CW complex called , then the fundamental group of will be .
Henri Poincaré's 1895 paper Analysis Situs studied three-and-higher-dimensional manifolds(which he called "varieties"), giving rigorous definitions of homology, homotopy (which had originally been defined in the context of late nineteenth-century knot theory, developed by Maxwell and others), and Betti numbers and raised a question, today known as the Poincaré conjecture, based his new concept of the fundamental group.