Are you an EPFL student looking for a semester project?
Work with us on data science and visualisation projects, and deploy your project as an app on top of GraphSearch.
Concept
Eilenberg–Ganea conjecture
Summary
The Eilenberg–Ganea conjecture is a claim in algebraic topology. It was formulated by Samuel Eilenberg and Tudor Ganea in 1957, in a short, but influential paper. It states that if a group G has cohomological dimension 2, then it has a 2-dimensional Eilenberg–MacLane space . For n different from 2, a group G of cohomological dimension n has an n-dimensional Eilenberg–MacLane space. It is also known that a group of cohomological dimension 2 has a 3-dimensional Eilenberg−MacLane space.
In 1997, Mladen Bestvina and Noel Brady constructed a group G so that either G is a counterexample to the Eilenberg–Ganea conjecture, or there must be a counterexample to the Whitehead conjecture; in other words, not both conjectures can be true.
Official source
About this result
This page is automatically generated and may contain information that is not correct, complete, up-to-date, or relevant to your search query. The same applies to every other page on this website. Please make sure to verify the information with EPFL's official sources.