Equivalences to the triangulation conjecture
Algebraic and Geometric Topology, Tome 2 (2002) no. 2, pp. 1147-1154
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We utilize the obstruction theory of Galewski–Matumoto–Stern to derive equivalent formulations of the Triangulation Conjecture. For example, every closed topological manifold Mn with n ≥ 5 can be simplicially triangulated if and only if the two distinct combinatorial triangulations of RP5 are simplicially concordant.

DOI : 10.2140/agt.2002.2.1147
Keywords: triangulation, Kirby–Siebenmann class, Bockstein operator, topological manifold

Randall, Duane  1

1 Department of Mathematics and Computer Science, Loyola University, New Orleans, LA 70118, USA
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Randall, Duane. Equivalences to the triangulation conjecture. Algebraic and Geometric Topology, Tome 2 (2002) no. 2, pp. 1147-1154. doi: 10.2140/agt.2002.2.1147

[1] R Fintushel, R J Stern, Instanton homology of Seifert fibred homology three spheres, Proc. London Math. Soc. $(3)$ 61 (1990) 109

[2] M Furuta, Homology cobordism group of homology 3–spheres, Invent. Math. 100 (1990) 339

[3] D E Galewski, R J Stern, Classification of simplicial triangulations of topological manifolds, Ann. of Math. $(2)$ 111 (1980) 1

[4] D Galewski, R Stern, A universal 5–manifold with respect to simplicial triangulations, from: "Geometric topology (Proc. Georgia Topology Conf., Athens, Ga., 1977)", Academic Press (1979) 345

[5] D E Galewski, R J Stern, Simplicial triangulations of topological manifolds, from: "Algebraic and geometric topology (Proc. Sympos. Pure Math., Stanford Univ., Stanford, Calif., 1976), Part 2", Proc. Sympos. Pure Math., XXXII, Amer. Math. Soc. (1978) 7

[6] , Problems in low-dimensional topology, from: "Geometric topology (Athens, GA, 1993)", AMS/IP Stud. Adv. Math. 2, Amer. Math. Soc. (1997) 35

[7] R C Kirby, L C Siebenmann, Foundational essays on topological manifolds, smoothings, and triangulations, Princeton University Press (1977)

[8] T Matumoto, Triangulation of manifolds, from: "Algebraic and geometric topology (Proc. Sympos. Pure Math., Stanford Univ., Stanford, Calif., 1976), Part 2", Proc. Sympos. Pure Math., XXXII, Amer. Math. Soc. (1978) 3

[9] R J Milgram, Some remarks on the Kirby–Siebenmann class, from: "Algebraic topology and transformation groups (Göttingen, 1987)", Lecture Notes in Math. 1361, Springer (1988) 247

[10] D Randall, On 4–dimensional bundle theories, from: "Differential topology, foliations, and group actions (Rio de Janeiro, 1992)", Contemp. Math. 161, Amer. Math. Soc. (1994) 217

[11] A A Ranicki, On the Hauptvermutung, from: "The Hauptvermutung book", $K$–Monogr. Math. 1, Kluwer Acad. Publ. (1996) 3

[12] Y B Rudyak, On Thom spectra, orientability, and cobordism, Springer Monographs in Mathematics, Springer (1998)

[13] L C Siebenmann, Are nontriangulable manifolds triangulable?, from: "Topology of Manifolds (Proc Inst., Univ. of Georgia, Athens, Ga., 1969)", Markham, Chicago, Ill. (1970) 77

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