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Stallings-Zeeman Theorem

If M^n is a finite simplicial complex of dimension n>=5 that has the homotopy type of the sphere S^n and is locally piecewise linearly homeomorphic to the Euclidean space R^n, then M^n is homeomorphic to S^n under a homeomorphism which is piecewise linear except at a single point. In other words, the complement M^n\(point) is piecewise linearly homeomorphic to R^n (Milnor).

See also

Poincaré Conjecture

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References

Milnor, J. "The Poincaré Conjecture." http://www.claymath.org/millennium/Poincare_Conjecture/Official_Problem_Description.pdf.Stallings, J. "The Piecewise-Linear Structure of Euclidean Space." Proc. Cambridge Philos. Soc. 58, 481-488, 1962.Zeeman, E. C. "The Generalised Poincaré Conjecture." Bull. Amer. Math. Soc. 67, 270, 1961.Zeeman, E. C. "The Poincaré Conjecture for n>=5." In Topology of 3-Manifolds and Related Topics, Proceedings of the University of Georgia Institute, 1961. Englewood Cliffs, NJ: Prentice-Hall, pp. 198-204, 1961.

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Stallings-Zeeman Theorem

Cite this as:

Weisstein, Eric W. "Stallings-Zeeman Theorem." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/Stallings-ZeemanTheorem.html

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