Abstract
An A kn -polyhedron is a CW-complex which is (n−1)-connected and of dimension ≤(n+k). We compute an algebraic category which is equivalent to the homotopy category of A 2n -polyhedra with free homology (n≥3). This computation and a calculation of the Γ-group Γn+3(X) (n≥3) is used to obtain a complete algebraic homotopy invariant for A 4n -polyhedra with free homology (n≥3).
As an application we compute the group of self-homotopy equivalences Aut(X) for a bouquet X=∨∑ℂP2.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Baues, H.J.: Algebraic Homotopy. Cambridge University Press (1989)
Baues, H.J.: Commutator Calculus and Groups of Homotopy Classes. Lecture Notes of the London Math. Soc. No. 50, 1981
Baues, H.J.: Homological Algebra of Quadratic Functors. Preprint, Bonn (1989)
Baues, H.J.: Obstruction Theory. Lecture Notes in Mathematics 628. Springer Verlag, Berlin Heidelbarg New York, (1977)
Chang, S.C.: Homotopy Invariants and Continuous Mappings. Proc. Royal Soc. London. Ser. A. 202, 256–263, (1950)
Hartl, M.: Quadratische Funktoren und Homotopie von Moore Räumen. Diplomarbeit, Bonn (1985)
Toda, H.: Composition Methods in Homotopy Groups of Spheres. Annals of Mathematical Studies No. 49
Unsöld, H.M.: On the Classification of Spaces with Free Homology. Dissertation FU Berlin (1987)
Whitehead, G.W. Elements of Homotopy Theory. Graduate Texts in Mathematics 61. Springer Verlag, Berlin Heidelberg New York, (1978)
Whitehead, J.H.C.: A Certain Exact Sequence. Ann. of Math. 52, 51–110, (1950)
Yamaguchi, K.: The Group of Self-Homotopy Equivalences and the Homotopy Types. Preprint (1989)
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Unsöld, H.M. A 4n -polyhedra with free homology. Manuscripta Math 65, 123–145 (1989). https://doi.org/10.1007/BF01168295
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF01168295