
Recent Posts
 Groups quasiisometric to planes
 Div, grad, curl and all this
 A tale of two arithmetic lattices
 3manifolds everywhere
 kleinian, a tool for visualizing Kleinian groups
 Kähler manifolds and groups, part 2
 Kähler manifolds and groups, part 1
 Liouville illiouminated
 Scharlemann on Schoenflies
 You can solve the cube – with commutators!
 Chiral subsurface projection, asymmetric metrics and quasimorphisms
 Random groups contain surface subgroups
 wireframe, a tool for drawing surfaces
 Cube complexes, Reidemeister 3, zonohedra and the missing 8th region
 Orthocentricity
 Kenyon’s squarespirals
 Thurston talks on geometrization at Harvard
 Random turtles in the hyperbolic plane
 Surface subgroups of Sapir’s group
 Upper curvature bounds and CAT(K)
 Bill Thurston 19462012
 Circle packing – theory and practice
 Agol’s Virtual Haken Theorem (part 3): return of the hierarchies
 Agol’s Virtual Haken Theorem (part 2): AgolGrovesManning strike back
 Agol’s Virtual Haken Theorem (part 1)
Blogroll
 Area 777
 Combinatorics and more
 Deep street soul
 Evaluating EDiscovery
 floerhomology
 Gaddeswarup
 Geometric Group Theory
 Godel's lost letter and P=NP
 Images des mathematiques
 Jim Woodring
 Language Log
 Letters of note
 Low dimensional topology
 Math Overflow
 Mathematics under the microscope
 nCategory Cafe
 Noncommutative geometry
 Paul Krugman
 Persiflage
 Preposterous Universe
 Questionable content
 Quomodocumque
 Real Climate
 Scott McCloud
 Secret blogging seminar
 Sketches of topology
 T Calegari
 Tanya Khovanova
 Terry Tao
 Tim Gowers
 Tony Phillips
Books
Software
Recent Comments
Categories
 3manifolds (17)
 4manifolds (2)
 Algebraic Geometry (2)
 Biology (2)
 Commentary (4)
 Complex analysis (8)
 Convex geometry (2)
 Diophantine approximation (1)
 Dynamics (9)
 Ergodic Theory (8)
 Euclidean Geometry (8)
 Foliations (1)
 Geometric structures (5)
 Groups (30)
 Hyperbolic geometry (21)
 Knot theory (1)
 Lie groups (8)
 Number theory (1)
 Overview (2)
 Polyhedra (2)
 Probability (1)
 Projective geometry (1)
 Psychology (2)
 Riemannian geometry (1)
 Rigidity (2)
 Special functions (1)
 Surfaces (18)
 Symplectic geometry (2)
 TQFT (1)
 Uncategorized (5)
 Visualization (9)
Meta
Category Archives: 3manifolds
Groups quasiisometric to planes
I was saddened to hear the news that Geoff Mess recently passed away, just a few days short of his 54th birthday. I first met Geoff as a beginning graduate student at Berkeley, in 1995; in fact, I believe he gave the … Continue reading
Div, grad, curl and all this
The title of this post is a nod to the excellent and wellknown Div, grad, curl and all that by Harry Schey (and perhaps also to the lesserknown sequel to one of the more consoling histories of Great Britain), and the purpose … Continue reading
Posted in 3manifolds, Riemannian geometry
Tagged curl, div, exposition, grad, Riemannian geometry, vector field
4 Comments
3manifolds everywhere
When I started in graduate school, I was very interested in 3manifolds, especially Thurston’s geometrization conjecture. Somehow in dimension 3, there is a marvelous marriage of flexibility and rigidity: generic 3manifolds are flexible enough to admit hyperbolic structures — i.e. Riemannian metrics … Continue reading
Posted in 3manifolds, Groups, Hyperbolic geometry
Tagged 3manifolds, acylindrical, quasiconvex group, Random groups, Sierpinski carpet
Leave a comment
Scharlemann on Schoenflies
Yesterday and today Marty Scharlemann gave two talks on the Schoenflies Conjecture, one of the great open problems in low dimensional topology. These talks were very clear and inspiring, and I thought it would be useful to summarize what Marty … Continue reading
Cube complexes, Reidemeister 3, zonohedra and the missing 8th region
There is an old puzzle which starts by asking: what is the next number in the sequence 1,2,4,? We are supposed to recognize the start of the sequence and answer that the next number is surely 8, because the first … Continue reading
Agol’s Virtual Haken Theorem (part 3): return of the hierarchies
Ian gave his second and third talks this afternoon, completing his (quite detailed) sketch of the proof of the Virtual Haken Theorem. Recall that after work of KahnMarkovic, Wise, HaglundWise and BergeronWise, the proof reduces to showing the following: Theorem … Continue reading
Agol’s Virtual Haken Theorem (part 1)
I am in Paris attending a workshop at the IHP where Ian Agol has just given the first of three talks outlining his proof of the Virtual Haken Conjecture and Virtual Fibration Conjecture in 3manifold topology (hat tip to Henry … Continue reading