Please use this identifier to cite or link to this item: https://hdl.handle.net/1959.11/16791
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
Handle Link: https://hdl.handle.net/1959.11/16791
Open Access Link: https://arxiv.org/abs/1309.6510
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
1432-0622
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
Statistics to Oct 2018: Visitors: 596
Views: 602
Downloads: 7
Appears in Collections:Journal Article

Files in This Item:
2 files
File Description SizeFormat 
Show full item record

Page view(s)

46
checked on Dec 29, 2018
Google Media

Google ScholarTM

Check

Altmetric

SCOPUSTM   
Citations

 

WEB OF SCIENCETM
Citations

 

Items in Research UNE are protected by copyright, with all rights reserved, unless otherwise indicated.