Geodesic
Could the Poincar\'e Conjecture Be False?
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Geometric topology and set theory, Tome 247 (2004), pp. 247-251.

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Two conjectures are stated which imply that the Poincaré hypothesis (asserting that any simply connected closed compact $3$-manifold is the $3$-sphere) is false. The first one claims that, for certain classes of finitely presented groups, the triviality problem is algorithmically undecidable, and the second one claims that certain embeddings of two-dimensional polyhedra in $3$-manifolds can effectively be constructed. 
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A. B. Sosinskii. Could the Poincar\'e Conjecture Be False?. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Geometric topology and set theory, Tome 247 (2004), pp. 247-251. http://geodesic.mathdoc.fr/item/TM_2004_247_a17/

[1] Adyan S. I., “Algoritmicheskaya nerazreshimost problem raspoznavaniya nekotorykh svoistv grupp”, DAN SSSR, 103 (1955), 533–535 | MR | Zbl

[2] Fomenko A. T., Fuks D. B., Kurs gomotopicheskoi topologii, Nauka, M., 1989 | MR

[3] Hall M., Jr., The theory of groups, Macmillan, New York, 1959 ; Kholl M., Teoriya grupp, IL, M., 1962 | MR | Zbl

[4] Magnus W., Karrass A., Solitar D., Combinatorial group theory: Presentations of groups in terms of generators and relations, Intersci. Publ., New York, 1966 ; Magnus V., Karras A., Soliter D., Kombinatornaya teoriya grupp: Predstavlenie grupp v terminakh obrazuyuschikh i sootnoshenii, Nauka, M., 1974 | MR | MR | Zbl

[5] Matveev S. V., Algorithmic problems in 3-manifolds, Springer, Berlin, 2003 | MR

[6] Perelman G., The entropy formula for the Ricci flow and its geometric application, , 2002 arXiv: /math.DG/0211159

[7] Perelman G., Ricci flow with surgery on three-manifolds, , 2003 arXiv: /math.DG/0303109

[8] Rabin M., “Recursive unsolvability of group theoretic problems”, Ann. Math. Ser. 2, 67 (1958), 172–194 | DOI | MR | Zbl

[9] Rogers H., Jr., Theory of recursive functions and effective computation, McGraw Hill, New York, 1967 | MR | Zbl

[10] Sossinsky A. B., “Simply connected 3-manifolds and undecidable problems in group theory”, Russ. J. Math. Phys., 7 (2000), 357–362 | MR | Zbl