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Stephen John Bigelow (Born 21 September 1971) is an Associate Professor of Mathematics at the University of California, Santa Barbara, and a research in low dimensional topology.

Around 2001 Stephen Bigelow and Daan Krammer independently proved that all braid groups are linear. Their work used the Lawrence–Krammer representation of dimension n(n−1)/2 depending on the variables q and t. By suitably specializing these variables, the braid group Bn may be realized as a subgroup of the general linear group over the complex numbers.