Geodesic
Homotopy groups and twisted homology of arrangements
Randell, Richard1
1Department of Mathematics, University of Iowa, Iowa City, IA 52242, USA
Algebraic and Geometric Topology, Tome 9 (2009) no. 3, pp. 1299-1308
Cet article a éte moissonné depuis la source Mathematical Sciences Publishers

Voir la notice de l'article

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.

DOI : 10.2140/agt.2009.9.1299
Keywords: hyperplane arrangement, local system, twisted homology

Randell, Richard  1

1 Department of Mathematics, University of Iowa, Iowa City, IA 52242, USA 
@article{10_2140_agt_2009_9_1299,
     author = {Randell, Richard},
     title = {Homotopy groups and twisted homology of arrangements},
     journal = {Algebraic and Geometric Topology},
     pages = {1299--1308},
     year = {2009},
     volume = {9},
     number = {3},
     doi = {10.2140/agt.2009.9.1299},
     url = {http://geodesic.mathdoc.fr/articles/10.2140/agt.2009.9.1299/}
}
TY  - JOUR
AU  - Randell, Richard
TI  - Homotopy groups and twisted homology of arrangements
JO  - Algebraic and Geometric Topology
PY  - 2009
SP  - 1299
EP  - 1308
VL  - 9
IS  - 3
UR  - http://geodesic.mathdoc.fr/articles/10.2140/agt.2009.9.1299/
DO  - 10.2140/agt.2009.9.1299
ID  - 10_2140_agt_2009_9_1299
ER  - 
%0 Journal Article
%A Randell, Richard
%T Homotopy groups and twisted homology of arrangements
%J Algebraic and Geometric Topology
%D 2009
%P 1299-1308
%V 9
%N 3
%U http://geodesic.mathdoc.fr/articles/10.2140/agt.2009.9.1299/
%R 10.2140/agt.2009.9.1299
%F 10_2140_agt_2009_9_1299
Randell, Richard. Homotopy groups and twisted homology of arrangements. Algebraic and Geometric Topology, Tome 9 (2009) no. 3, pp. 1299-1308. doi: 10.2140/agt.2009.9.1299

[1] D C Cohen, Triples of arrangements and local systems, Proc. Amer. Math. Soc. 130 (2002) 3025

[2] D C Cohen, A Dimca, P Orlik, Nonresonance conditions for arrangements, Ann. Inst. Fourier (Grenoble) 53 (2003) 1883

[3] D C Cohen, A I Suciu, On Milnor fibrations of arrangements, J. London Math. Soc. $(2)$ 51 (1995) 105

[4] A Dimca, Ş Papadima, Hypersurface complements, Milnor fibers and higher homotopy groups of arrangments, Ann. of Math. $(2)$ 158 (2003) 473

[5] A Dimca, Ş Papadima, Equivariant chain complexes, twisted homology and relative minimality of arrangements, Ann. Sci. École Norm. Sup. $(4)$ 37 (2004) 449

[6] A Hatcher, Algebraic topology, Cambridge Univ. Press (2002)

[7] A Hattori, Topology of $C^{n}$ minus a finite number of affine hyperplanes in general position, J. Fac. Sci. Univ. Tokyo Sect. IA Math. 22 (1975) 205

[8] R Liu, On the classification of $(n-k+1)$–connected embeddings of $n$–manifolds into $(n+k)$-manifolds in the metastable range, Trans. Amer. Math. Soc. 347 (1995) 4245

[9] P Orlik, H Terao, Arrangements of hyperplanes, Grund. der Math. Wissenschaften 300, Springer (1992)

[10] R Randell, Homotopy and group cohomology of arrangements, Topology Appl. 78 (1997) 201

[11] R Randell, Morse theory, Milnor fibers and minimality of hyperplane arrangements, Proc. Amer. Math. Soc. 130 (2002) 2737

[12] M Yoshinaga, Generic section of a hyperplane arrangement and twisted Hurewicz maps, Topology Appl. 155 (2008) 1022

Cité par Sources :