If 
is a differentiable homotopy
sphere of dimension 
,
then 
is homeomorphic to 
.
In fact, 
is diffeomorphic to a manifold obtained by gluing together the boundaries of two
closed 
-balls
under a suitable diffeomorphism (Milnor).
Smale Theorem
See also
Freedman Theorem, Poincaré ConjectureExplore with Wolfram|Alpha
References
Milnor, J. "The Poincaré Conjecture." http://www.claymath.org/millennium/Poincare_Conjecture/Official_Problem_Description.pdf.Smale, S. "Generalized Poincaré's Conjecture in Dimensions Greater than Four." Ann. Math. 74, 391-406, 1961.Referenced on Wolfram|Alpha
Smale TheoremCite this as:
Weisstein, Eric W. "Smale Theorem." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/SmaleTheorem.html