The topological Borel conjecture asserts that every homotopy equivalence between closed aspherical manifolds is homotopic to a homeomorphism. It predicts rigidity within each prescribed homotopy class. The weaker homeomorphism-existence formulation asks only whether homotopy-equivalent closed aspherical manifolds are homeomorphic.
Borel Conjecture
See also
Aspherical Space, Fundamental Group, Homeomorphism, Homotopy Equivalence, Hyperbolic Group, ManifoldExplore with Wolfram|Alpha
References
Lück, W. and Reich, H. "The Baum-Connes and the Farrell-Jones Conjectures in
- and 
-Theory." In Handbook of K-Theory, Vol. 2
(Ed. E. M. Friedlander and D. R. Grayson). Berlin, Germany: Springer,
pp. 703-842, 2005. https://doi.org/10.1007/978-3-540-27855-9_15.
Cite this as:
Weisstein, Eric W. "Borel Conjecture." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/BorelConjecture.html