3-manifolds and number fields
Adam Sikora Principal Investigator
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DMS-0307078<br/>Adam Sikora<br/><br/>Thirty years ago B. Mazur discovered some surprising <br/>similarities (a) between knots and prime numbers, and (b) between<br/>3-dimensional manifolds and number fields. Those similarities were<br/>further elaborated by Kapranov, Morishita, Ramachandran, Reznikov, and<br/>PI, but the full scope of these analogies is still unknown. <br/>PI's goal is to continue investigation of these analogies and their <br/>roots.<br/><br/>Arithmetic topology is an exiting new area of mathematical research<br/>relating two of the most active areas of mathematical research<br/>in the recent years: low-dimensional topology and number theory. <br/>The development of Arithmetic Topology is driven by the desire to <br/>establish<br/>rigorous and uniform foundations for those two seemingly diverse <br/>theories.