Stallings-Zeeman theorem

In mathematics, the Stallings-Zeeman theorem is a result in algebraic topology, used in the proof of the Poincaré conjecture for dimension greater than or equal to five. It is named after the mathematicians John Stallings and Erik Christopher Zeeman.

tatement of the theorem

Let "M" be a finite simplicial complex of dimension dim("M") = "m" ≥ 5. Suppose that "M" has the homotopy type of the "m"-dimensional sphere S^"m" and that "M" is locally piecewise linearly homeomorphic to "m"-dimensional Euclidean space R^"m". Then "M" is homeomorphic to S^"m" under a map that is piecewise linear except possibly at a single point "x". That is, "M" {"x"} is piecewise linearly homeomorphic to R^"m".

References

* cite journal
last = Stallings
first = John
title = The piecewise-linear structure of Euclidean space
journal = Proc. Cambridge Philos. Soc.
volume = 58
year = 1962
pages = 481–488 MathSciNet|id=0149457
* cite journal
last = Zeeman
first = Erik Christopher
authorlink= Erik Christopher Zeeman
title = The generalised Poincaré conjecture
journal = Bull. Amer. Math. Soc.
volume = 67
year = 1961
pages = 270
doi = 10.1090/S0002-9904-1961-10578-8 MathSciNet|id=0124906