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The homotopy type of a combinatorially aspherical presentation. (English) Zbl 0421.55004

MSC:
55P15 Classification of homotopy type
57M20 Two-dimensional complexes (manifolds) (MSC2010)
57M05 Fundamental group, presentations, free differential calculus
55Q52 Homotopy groups of special spaces
55S45 Postnikov systems, \(k\)-invariants
20F05 Generators, relations, and presentations of groups
20F65 Geometric group theory
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References:
[1] Adams, J.F.: Four applications of the self-obstruction invariants. J. London Math. Soc.31, 148-159 (1956) · Zbl 0071.16501 · doi:10.1112/jlms/s1-31.2.148
[2] Brown, R., Higgins, P.J.: On the connection between the second relative homotopy groups of some related spaces. Proc. London Math. Soc. (3)36, 193-212 (1978) · Zbl 0405.55015 · doi:10.1112/plms/s3-36.2.193
[3] Chiswell, I.M., Collins, D.J., Huebschmann, J.: Aspherical group presentations. Preprint · Zbl 0443.20030
[4] Eilenberg, S., Mac Lane, S.: Homology of spaces with operators. II. Trans. Amer. Math. Soc.65, 49-99 (1949) · Zbl 0034.11101 · doi:10.1090/S0002-9947-1949-0033001-0
[5] Huebschmann, J.: Cohomology theory of aspherical groups and of small cancellation groups. J. Pure Appl. Algebra14, 137-143 (1979) · Zbl 0396.20021 · doi:10.1016/0022-4049(79)90003-3
[6] Huebschmann, J.: The firstk-invariant, Quillen’s spaceBG + and the construction of Kan and Thurston. Comment. Math. Helv.55, 314-318 (1980) · Zbl 0443.18017 · doi:10.1007/BF02566689
[7] Lyndon, R.: Cohomology theory of groups with a single defining relation. Ann. of Math.52, 650-665 (1950) · Zbl 0039.02302 · doi:10.2307/1969440
[8] Lyndon, R., Schupp, P.E.: Combinatorial group theory. Ergebnisse der Mathematik und ihrer Grenzgebiete89. Berlin-Heidelberg-New York: Springer 1977 · Zbl 0368.20023
[9] Whitehead, J.H.C.: Combinatorial homotopy. II. Bull. Amer. Math. Soc.55, 453-496 (1949) · Zbl 0040.38801 · doi:10.1090/S0002-9904-1949-09213-3
[10] Whitehead, J.H.C.: TheG-dual of a semi-exact couple. Proc. London Math. Soc. (3)3, 385-416 (1953) · Zbl 0052.39801 · doi:10.1112/plms/s3-3.1.385
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