Geodesic
Knotting of contractible two-dimensional polyhedra in~$\mathbf R^4$
Sbornik. Mathematics, Tome 18 (1972) no. 2, pp. 333-341

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In this paper the Zeeman conjecture that any piecewise linear embedding of the dunce's hat (i.e. the triangle $ABC$ with the oriented edges $AB$, $BC$, and $AC$ identified) in $\mathbf R^4$ has simply connected complement is disproven. Indeed, the author constructs linear embeddings in $\mathbf R^4$ with non-simply-connected complements for a class of two-dimensional polyhedra. All of these, just as the dunce's hat, are contractible but not combinatorially contractible, and the author ventures to conjecture that any two-dimensional polyhedra with these properties admits a piecewise linear embedding in $\mathbf R^4$ with non-simply-connected complement. Figures: 4. Bibliography: 7 titles. 
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     author = {S. A. Popov},
     title = {Knotting of contractible two-dimensional polyhedra in~$\mathbf R^4$},
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     number = {2},
     year = {1972},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1972_18_2_a11/}
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S. A. Popov. Knotting of contractible two-dimensional polyhedra in~$\mathbf R^4$. Sbornik. Mathematics, Tome 18 (1972) no. 2, pp. 333-341. http://geodesic.mathdoc.fr/item/SM_1972_18_2_a11/