Algebraic & Geometric Topology

Homotopy groups and twisted homology of arrangements

Richard Randell

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Abstract

Recent work of M Yoshinaga [Topology Appl. 155 (2008) 1022-1026] shows that in some instances certain higher homotopy groups of arrangements map onto nonresonant homology. This is in contrast to the usual Hurewicz map to untwisted homology, which is always the zero homomorphism in degree greater than one. In this work we examine this dichotomy, generalizing both results.

Article information

Source
Algebr. Geom. Topol., Volume 9, Number 3 (2009), 1299-1308.

Dates
Received: 30 December 2008
Revised: 5 May 2009
Accepted: 6 May 2009
First available in Project Euclid: 20 December 2017

Permanent link to this document
https://projecteuclid.org/euclid.agt/1513797030

Digital Object Identifier
doi:10.2140/agt.2009.9.1299

Mathematical Reviews number (MathSciNet)
MR2520401

Zentralblatt MATH identifier
1173.55003

Subjects
Primary: 55N25: Homology with local coefficients, equivariant cohomology 57N65: Algebraic topology of manifolds
Secondary: 55Q52: Homotopy groups of special spaces

Keywords
hyperplane arrangement local system twisted homology

Citation

Randell, Richard. Homotopy groups and twisted homology of arrangements. Algebr. Geom. Topol. 9 (2009), no. 3, 1299--1308. doi:10.2140/agt.2009.9.1299. https://projecteuclid.org/euclid.agt/1513797030


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References

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