
Recent Posts
 Bing’s wild involution
 StiefelWhitney cycles as intersections
 Schläfli – for lush, voluminous polyhedra
 Slightly elevated Teichmuller theory
 Mr Spock complexes (after Aitchison)
 Roots, Schottky semigroups, and Bandt’s Conjecture
 Taut foliations and positive forms
 Explosions – now in glorious 2D!
 Dipoles and Pixie Dust
 Mapping class groups: the next generation
 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
Blogroll
 0xDE
 Area 777
 Bluefawnpinkmanga
 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
 Math/Art Blog
 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
 Tanya Khovanova
 Terry Tao
 Tim Gowers
 Tony Phillips
Books
Software
Recent Comments
Larry Taylor on Scharlemann on Schoenflies Anton Izosimov on How to see the genus Adam Wood on How to see the genus Constancy of the spe… on Measure theory, topology, and… Torsten on Circle packing – theory… Categories
 3manifolds (21)
 4manifolds (2)
 Algebraic Geometry (2)
 Algebraic Topology (1)
 Biology (2)
 Commentary (4)
 Complex analysis (11)
 Convex geometry (2)
 Diophantine approximation (1)
 Dynamics (13)
 Ergodic Theory (8)
 Euclidean Geometry (8)
 Foliations (2)
 Geometric structures (6)
 Groups (31)
 Hyperbolic geometry (25)
 Knot theory (1)
 Lie groups (8)
 Number theory (2)
 Overview (2)
 Polyhedra (3)
 Probability (1)
 Projective geometry (2)
 Psychology (3)
 Riemannian geometry (1)
 Rigidity (2)
 Special functions (2)
 Surfaces (20)
 Symplectic geometry (3)
 TQFT (1)
 Uncategorized (6)
 Visualization (10)
Meta
Author Archives: Danny Calegari
Bing’s wild involution
An embedded circle separates the sphere into two connected components; this is the Jordan curve theorem. A strengthening of this fact, called the JordanSchoenflies theorem, says that the two components are disks; i.e. every embedded circle in the sphere bounds a … Continue reading
Posted in 3manifolds, Uncategorized
Tagged Alexander horned sphere, Bing, wild involution
2 Comments
StiefelWhitney cycles as intersections
This quarter I’m teaching the “Differential Topology” firstyear graduate class, and for a bit of fun, I decided to teach an introduction to characteristic classes, following the classic book of that name by Milnor and Stasheff. The book begins with … Continue reading
Schläfli – for lush, voluminous polyhedra
Because of some turbulence in real life (™) over the last few months, it’s been somewhat hard to concentrate on research. Fortunately the obligation of teaching sometimes exerts the right sort of psychological pressure to keep my mind on mathematics in short bursts. Continue reading
Slightly elevated Teichmuller theory
Last week at my invitation, David Dumas spoke in the U Chicago geometry seminar and gave a wonderful introductory talk on the theory of convex real projective structures on surfaces. This is the first step on the road to what is colloquially known … Continue reading
Mr Spock complexes (after Aitchison)
The recent passing of Leonard Nimoy prompts me to recall a lesserknown connection between the great man and the theory of (cusped) hyperbolic 3manifolds, observed by my friend and former mentor Iain Aitchison. In particular, I am moved to give a brief presentation … Continue reading
Taut foliations and positive forms
This week I visited Washington University in St. Louis to give a colloquium, and caught up with a couple of my old foliations friends, namely Rachel Roberts and Larry Conlon. Actually, I had caught up with Rachel (to some extent) … Continue reading