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Monthly Archives: October 2009
Bridgeman’s orthospectrum identity
Martin Bridgeman gave a nice talk at Caltech recently on his discovery of a beautiful identity concerning orthospectra of hyperbolic surfaces (and manifolds of higher dimension) with totally geodesic boundary. The dimensional case is (in my opinion) the most beautiful, … Continue reading
SchwarzChristoffel transformations, Schwarzian derivatives, and Schwarz’s minimal surface
Hermann Amandus Schwarz (18431921) was a student of Kummer and Weierstrass, and made many significant contributions to geometry, especially to the fields of minimal surfaces and complex analysis. His mathematical creations are both highly abstract and flexible, and at the … Continue reading
Quasimorphisms from knot invariants
Last week, Michael Brandenbursky from the Technion gave a talk at Caltech on an interesting connection between knot theory and quasimorphisms. Michael’s paper on this subject may be obtained from the arXiv. Recall that given a group , a quasimorphism … Continue reading
Posted in 3manifolds, Groups
Tagged 4ball genus, braids, CochranOrrTeichner, knot concordance, quasimorphisms, ribbon, signature, slice
2 Comments
Harmonic measure
An amenable group acting by homeomorphisms on a compact topological space preserves a probability measure on ; in fact, one can given a definition of amenability in such terms. For example, if is finite, it preserves an atomic measure supported … Continue reading