In mathematics, specifically geometric topology, the Borel conjecture asserts that an aspherical closed manifold is determined by its fundamental group, up to homeomorphism. It is a rigidity conjecture, demanding that a weak, algebraic notion of equivalence (namely, a homotopy equivalence) imply a stronger, topological notion (namely, a homeomorphism).
Read more about Borel Conjecture: Precise Formulation of The Conjecture, The Origin of The Conjecture, Motivation For The Conjecture, Relationship To Other Conjectures
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“There is something fascinating about science. One gets such wholesale returns of conjecture out of such a trifling investment of fact.”
—Mark Twain [Samuel Langhorne Clemens] (1835–1910)