Peter B. Shalen (born c. 1946) is an American mathematician, working primarily in low-dimensional topology.
[4] He was elected as a member of the 2017 class of Fellows of the American Mathematical Society "for contributions to three-dimensional topology and for exposition".
[5] His work with Marc Culler related properties of representation varieties of hyperbolic 3-manifold groups to decompositions of 3-manifolds.
Based on this work, Culler, Cameron Gordon, John Luecke, and Shalen proved the cyclic surgery theorem.
With John W. Morgan, he generalized his work with Culler, and reproved several foundational results of William Thurston.