In geometric topology, the Borel conjecture asserts that an aspherical closed manifold is determined by its fundamental group, up to homeomorphism. This description is adapted from Wikipedia contributors under CC BY-SA 4.0; changes were made. https://creativecommons.org/licenses/by-sa/4.0/
Facts
StatementAn aspherical closed manifold is determined by its fundamental group, up to homeomorphism. 1 Proposed Year Progress Toward ResolutionThe conjecture is false if topological manifolds and homeomorphisms are replaced by smooth manifolds and diffeomorphisms. 1 Classification
Resolution Status Prize Status
Prize Status (category) Connections
In Branch
Source Borel Conjecture (Wikipedia)
Sources
1. Borel Conjecture (Wikipedia)
Wikimedia FoundationLead section
May 1953, in a letter to Jean-Pierre Serre
Precise formulation of the conjecture
This conjecture is false if topological manifolds and homeomorphisms are replaced by smooth manifolds and diffeomorphisms.
Lead section, first sentence
an aspherical closed manifold is determined by its fundamental group, up to homeomorphism
In Branch: Geometric Topology, Lead sentence
In geometric topology, the Borel conjecture (named for Armand Borel) asserts that an aspherical closed manifold is determined by i
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