One-dimensional sets and planar sets are aspherical

By James W. Cannon, Gregory R. Conner, A. Zastrow. 2002

46 citations recorded by the source corpus.

Subfields: Computational Theory and Mathematics, Computer Graphics and Computer-Aided Design, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/74db51673c53029495d2125992335a998df2ffb6

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Computational Theory and Mathematics

1. James W. Cannon
2. Gregory R. Conner
3. J. Heinonen
4. Danny Calegari

In Geometry and Topology

1. Gregory R. Conner
2. James W. Cannon
3. J. Heinonen
4. R. Korte
5. Romain Tessera
6. Bruce Kleiner
7. Dachun Yang
8. Assaf Naor

Citations in the corpus

• Lectures on Lipschitz analysis (2005, background): “Miller’s result is a Lipschitz version of the fact that every planar set is aspherical, meaning that all the homotopy groups beyond the first two are trivial for such a set. See [ 12 ].”
• On the fundamental groups of one-dimensional spaces ✩ (2006, background): “Other papers in this general area we are aware of are [5], where it is shown that planar sets are aspherical, and a preprint of Bogley and Sieradski [1], in which they study one-dimensional metric cell complexes in which one-cells can limit on zero-cells.”