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Title: The third homotopy group as a π₁-module
Contributor(s): Baues, Hans-Joachim (author); Bleile, Beatrice (author)
Publication Date: 2015
Open Access: Yes
DOI: 10.1007/s00200-014-0240-5
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Abstract: It is well-known how to compute the structure of the second homotopy group of a space, X, as a module over the fundamental group π₁X, using the homology of the universal cover and the Hurewicz isomorphism. We describe a new method to compute the third homotopy group, π₃X as a module over π₁X. Moreover, we determine π₃X as an extension of π₁X-modules derived from Whitehead's Certain Exact Sequence. Our method is based on the theory of quadratic modules. Explicit computations are carried out for pseudo-projective 3-spaces X=S¹Ue²Ue³ consisting of exactly one cell in each dimension ≤ 3.
Publication Type: Journal Article
Source of Publication: Applicable Algebra in Engineering, Communication and Computing, 26(1-2), p. 165-189
Publisher: Springer
Place of Publication: Germany
ISSN: 0938-1279
Field of Research (FOR): 010299 Applied Mathematics not elsewhere classified
010112 Topology
010101 Algebra and Number Theory
Peer Reviewed: Yes
HERDC Category Description: C1 Refereed Article in a Scholarly Journal
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