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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

On simplicial resolutions of framed links


Authors: Fengchun Lei, Fengling Li and Jie Wu
Journal: Trans. Amer. Math. Soc. 366 (2014), 3075-3093
MSC (2010): Primary 57M25, 55P35; Secondary 55Q40, 55U10, 57M07
Published electronically: December 3, 2013
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Abstract: In this paper, we investigate the simplicial groups obtained from the link groups of naive cablings on any given framed link. Our main result states that the resulting simplicial groups have the homotopy type of the loop space of a wedge of $ 3$-spheres. This gives simplicial group models for some loop spaces using link groups.


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Additional Information

Fengchun Lei
Affiliation: School of Mathematical Sciences, Dalian University of Technology, Dalian 116024, People’s Republic of China
Email: fclei@dlut.edu.cn

Fengling Li
Affiliation: School of Mathematical Sciences, Dalian University of Technology, Dalian 116024, People’s Republic of China
Email: dutlfl@163.com

Jie Wu
Affiliation: Department of Mathematics, National University of Singapore, Block S17, 10 Lower Kent Ridge Road, Singapore 119076
Email: matwuj@nus.edu.sg

DOI: http://dx.doi.org/10.1090/S0002-9947-2013-05957-0
PII: S 0002-9947(2013)05957-0
Keywords: Framed link, simplicial group, link group, naive cabling, loop space
Received by editor(s): May 14, 2012
Received by editor(s) in revised form: September 9, 2012
Published electronically: December 3, 2013
Additional Notes: The first author was partially supported by a key grant (No.10931005) of NSFC and a grant (No.11329101) of NSFC
The second author was supported by two grants (No.11101058) and (No.11329101) of NSFC and a grant (No.2011M500049) of China Postdoctoral Science Foundation
The third author was partially supported by the AcRF Tier 2 (WB NO. R-146-000-143-112) of MOE of Singapore and a grant (No. 11329101) of NSFC
Article copyright: © Copyright 2013 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.