13 citations · 31 across the 7 of their papers we have counts for
7 papers
On the genus of infinite groups
Iain Aitchison, Lawrence Reeves
We associate to each finite presentation of a group G a compact CW-complex that is a 3-manifold in the complement of a point, and whose fundamental group is isomorphic to G. We use…
The geometry of oriented cubes
Iain R. Aitchison
This reports on the fundamental objects revealed by Ross Street, which he called `orientals'. Street's work was in part inspired by Robert's attempts to use N-category ideas to con…
Cusped hyperbolic 3-manifolds: canonically CAT(0) with CAT(0) spines
Iain R. Aitchison
We prove that every finite-volume hyperbolic 3-manifold M with p > 0 cusps admits a canonical, complete, piecewise Euclidean CAT(0) metric, with a canonical projection to a CAT(0)…
All finitely presentable groups from link complements and Kleinian groups
Iain R. Aitchison
We prove that every finitely presentable group G arises as the fundamental group of an orientable 3-complex obtained from a hyperbolic link complement, by coning each boundary toru…
The `Holiverse': holistic eversion of the 2-sphere in
Iain R. Aitchison
We give a short, simple and conceptual proof, based on spin structures, of sphere eversion: an embedded 2-sphere in can be turned inside out by regular homotopy. Ingredients…
Combinatorial Dehn surgery on cubed and Haken 3-manifolds
Iain R. Aitchison, J. Hyam Rubinstein
A combinatorial condition is obtained for when immersed or embedded incompressible surfaces in compact 3-manifolds with tori boundary components remain incompressible after Dehn su…