Bruce Hughes

Professor of Mathematics                                                  Photo

Department of Mathematics
Vanderbilt University, Nashville, TN 37240

Office: Stevenson Center 1528
Phone: (615) 322-6660
Email: bruce DOT hughes AT vanderbilt DOT edu
Office Hours: Fall 2010 TBA

Research Interests: Geometric and Algebraic Topology, Manifold Theory, Controlled Topology, Stratified Spaces, Continua Theory, Metric Spaces, Noncommutative Geometry, Geometric Group Theory

Preprints:

• Trees, ultrametrics, and noncommutative geometry. Pure and Applied Mathematical Quarterly (to appear), 60 pages, PDF, arXive
• Dihedral manifold approximate fibrations over the circle (with Qayum Khan). Geometrae Dedicata (to appear), 38 pages, PDF, arXive
• Bounded distortion homeomorphisms on ultrametric spaces (with Álvaro Martínez-Pérez and Manuel A. Morón). Annales Academiae Scientiarum Fennicae Mathematica (to appear), 20 pages, PDF, arXive

Books:

• Ends of Complexes (with Andrew Ranicki). Cambridge Tracts in Mathematics 123, Cambridge Univ. Press, Cambridge, 1996, xxvi+353 pages.
  Introduction (PDF) Errata (PDF) Geoghegan's Mathematical Reviews review (PDF) Munkholm's Zentralblatt review (PDF)
  
• Control and Relaxation over the Circle (with Stratos Prassidis). Memoirs of the American Mathematical Society, Volume 145, number 691, May 2000, ix+96 pages.
  Ranicki's Mathematical Reviews review (PDF)

Ten Selected Publications:

• Local similarities and the Haagerup property (with an appendix by D. S. Farley). Groups, Geometry, Dynamics, , PDF
• Examples of exotic stratifications (with L. Taylor, S. Weinberger and B. Williams), Geometry & Topology, (vol. 11, pp. 1477-1505, 2007); PDF
• Trees and ultrametric spaces: a categorical equivalence, Advances in Mathematics, (vol. 189, pp. 148-191, 2004); PDF, Figures, ScienceDirect Link
• Neighborhoods of strata in manifold stratified spaces, Glasgow Mathematical Journal (vol. 46, pp. 1-28, 2004);  PDF
• The approximate tubular neighborhood theorem, Annals of Mathematics (vol. 156, pp. 867-889, November 2002);   PDF
• Products and adjunctions of manifold stratified spaces, Topology and its Applications (vol. 124, pp 47-67, October 2002);  ScienceDirect Link
• Neighborhoods in stratified spaces with two strata (with L. Taylor, S. Weinberger and B. Williams), Topology 39 (2000), 873-919; ScienceDirect Link
• Surgery and stratified spaces (with S. Weinberger), in Surveys on Surgery Theory (S. Cappell, A. Ranicki and J. Rosenberg, eds.), vol. 2, Princeton Univ. Press, Princeton, 2000, pp. 311-342; PDF
• Controlled homeomorphisms over nonpositively curved manifolds (with L. Taylor and B. Williams),  Canadian Mathematical Bulletin; PDF
• Stratifications of teardrops, Fundamenta Mathematicae,(vol. 94, pp.305-324,  1999).

Other Publications

Collaborators:

• Dan Farley
• Rudy Gordh
• Qayum Khan
• Álvaro Martínez-Pérez
• Manuel A. Morón
• Stratos Prassidis
• Andrew Ranicki
• Larry Taylor
• Shmuel Weinberger
• Bruce Williams
  

Links:

• Topology & Group Theory Seminar, Vanderbilt University
• Workshop on Nil Phenomena in Topology, Vanderbilt University, 14-15 April 2007
• Research Group in Noncommutative Geometry and Operator Algebras at Vanderbilt

Courses:

• Math 205a: Multivariable Calculus and Linear Algebra
• Math 205b: Multivariable Calculus and Linear Algebra
• Math 242: Introduction to Topology
• Math 312: Algebraic Topology

Updated 31 May 2010