Bryn Mawr College

Paul Melvin

Research Field:     Geometry / Topology

    Interests:    Topology of 3 and 4-dimensional manifolds
                               knot theory & quantum topology

Recent Publications    (click here for a complete list)

• Generalized Gauss maps and integrals for three-component links: toward higher helicities for magnetic fields and fluid flows, Part I and Part II
   (with D. DeTurck, H. Gluck, R. Komendarczyk, C. Shonkwiler, S. Vela-Vick, and - for Part II - H. Nuchi) J. Mathematical Physics (part I) and
  Algebraic & Geometric Topology (part II)  2013 
• Cohomotopy sets of 4-manifolds  (with R. Kirby and P. Teichner)
  Geometry & Topology Monographs  2012 
• The Milnor degree of a 3-manifold  (with T. Cochran) J. Topology  2010 
• Triple linking numbers, ambiguous Hopf invariants and integral formulas for three component links  (with D. DeTurck, H. Gluck, R. Komendarczyk,
  C. Shonkwiler and S. Vela-Vick) Matematica Contemporanea  2009 
• Non-smoothable four-manifolds with infinite cyclic fundamental groups  (with S. Friedl, I. Hambleton and P. Teichner) IMRN  2007 
• A topological menagerie AMS Monthly  2006 
• The nonuniqueness of Chekanov polynomials of Legendrian knots  
  (with S. Shrestha) Geometry & Topology  2005 
• Local surgery formulas for quantum invariants and the Arf invariant  
  (with R. Kirby) Geometry & Topology Monographs  2004 
• A geometric interpretation of Milnor's triple linking numbers  
  (with B. Mellor) Algebraic & Geometric Topology  2003 
• Quantum cyclotomic orders of 3-manifolds  
  (with T. Cochran) Topology  2001 
• Finite type invariants of 3-manifolds  
  (with T. Cochran) Inventiones Mathematicae  2000 

Teaching

    Fall 2013           Introduction to Topology and Geometry (Math 221)

                            Senior Conference (Math 398)

    Spring 2014      On Sabbatical Leave