Abstract
We study the stable homotopy types of F 4 n(2) -polyhedra, i.e., (n − 1)-connected, at most (n + 4)-dimensional polyhedra with 2-torsion free homologies. We are able to classify the indecomposable F 4 n(2) -polyhedra. The proof relies on the matrix problem technique which was developed in the classification of representations of algebras and applied to homotopy theory by Baues and Drozd (1999, 2001, 2004).
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Baues H J, Drozd Y A. The homotopy classification of (n - 1)-connected (n + 4)-dimensional polyhedra with torsion free homology, n ≥ 5. Expo Math, 1999, 17: 161–180
Baues H J, Drozd Y A. Classification of stable homotopy types with torsion-free homology. Topology, 2001, 40: 789–821
Baues H J, Hennes M. The homotopy classification of (n-1)-connected (n+3)-dimensional polyhedra, n ≥ 4. Topology, 1991, 30: 373–408
Chang S C. Homotogy invariants and continuous mappings. Proc R Soc Lond Ser A Math Phys Eng Sci, 1950, 202: 253–263
Cohen J M. Stable Homotopy. Berlin-Heidelberg-New York: Springer-Verlag, 1970
Drozd Y A. Matrix problems and stable homotopy types of polyhedra. Cent Eur J Math, 2004, 2: 420–447
Drozd Y A. On classification of torsion free polyhedra. Http://www.imath.kiev.ua/~drozd/TFpoly.pdf, 2005
Drozd Y A. Matrix problems, triangulated categories and stable homotopy types. Sao Paulo J Math Sci, 2010, 4: 209–249
Pan J Z, Zhu Z J. The classification of 2 and 3 torsion free polyhedra. Acta Math Sin Engl Ser, 2015, 31: 1659–1682
Shimura G. Introduction to the Arithmetic Theory of Automorphic Functions. Princeton: Princeton University Press, 1971
Switzer R M. Algebraic Topology-Homology and Homotopy. Berlin: Springer-Verlag, 1975
Unsöld H M. A 4n -polyhedra with free homology. Manuscripta Math, 1989, 65: 123–146
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Pan, J., Zhu, Z. Stable homotopy classification of A 4 n -polyhedra with 2- torsion free homology. Sci. China Math. 59, 1141–1162 (2016). https://doi.org/10.1007/s11425-016-5123-8
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DOI: https://doi.org/10.1007/s11425-016-5123-8