Equivariant chain complexes, twisted homology and relative minimality of arrangements

Alexandru Dimca; Ştefan Papadima

Annales scientifiques de l'École Normale Supérieure (2004)

  • Volume: 37, Issue: 3, page 449-467
  • ISSN: 0012-9593

How to cite


Dimca, Alexandru, and Papadima, Ştefan. "Equivariant chain complexes, twisted homology and relative minimality of arrangements." Annales scientifiques de l'École Normale Supérieure 37.3 (2004): 449-467. <http://eudml.org/doc/82636>.

author = {Dimca, Alexandru, Papadima, Ştefan},
journal = {Annales scientifiques de l'École Normale Supérieure},
language = {eng},
number = {3},
pages = {449-467},
publisher = {Elsevier},
title = {Equivariant chain complexes, twisted homology and relative minimality of arrangements},
url = {http://eudml.org/doc/82636},
volume = {37},
year = {2004},

AU - Dimca, Alexandru
AU - Papadima, Ştefan
TI - Equivariant chain complexes, twisted homology and relative minimality of arrangements
JO - Annales scientifiques de l'École Normale Supérieure
PY - 2004
PB - Elsevier
VL - 37
IS - 3
SP - 449
EP - 467
LA - eng
UR - http://eudml.org/doc/82636
ER -


  1. [1] Cohen D, Cohomology and intersection cohomology of complex hyperplane arrangements, Adv. Math.97 (1993) 231-266. Zbl0787.57014MR1201844
  2. [2] Cohen D, Dimca A, Orlik P, Nonresonance conditions for arrangements, Annales Institut Fourier53 (2003) 1883-1896. Zbl1054.32016MR2038782
  3. [3] Cohen D, Orlik P, Arrangements and local systems, Math. Res. Lett.7 (2000) 299-316. Zbl0971.32012MR1764324
  4. [4] Cohen D, Suciu A, On Milnor fibrations of arrangements, J. London Math. Soc.51 (1995) 105-119. Zbl0814.32007MR1310725
  5. [5] Cohen D, Suciu A, The braid monodromy of plane algebraic curves and hyperplane arrangements, Comment. Math. Helv.72 (1997) 285-315. Zbl0959.52018MR1470093
  6. [6] Cohen D, Suciu A, Homology of iterated semidirect products of free groups, J. Pure Appl. Algebra126 (1998) 87-120. Zbl0908.20033MR1600518
  7. [7] Dimca A, Némethi A, Hypersurface complements, Alexander modules and monodromy, preprint , math.AG/0201291. Zbl1067.14004MR1747272
  8. [8] Dimca A, Papadima S, Hypersurface complements, Milnor fibers and higher homotopy groups of arrangements, Ann. Math.158 (2003) 473-507. Zbl1068.32019MR2018927
  9. [9] Eisenbud D, Commutative Algebra with a View Toward Algebraic Geometry, in: Grad. Texts in Math., vol. 150, Springer-Verlag, New York, 1995. Zbl0819.13001MR1322960
  10. [10] Falk M, Randell R, The lower central series of a fiber-type arrangement, Invent. Math.82 (1985) 77-88. Zbl0574.55010MR808110
  11. [11] Gibson C.G, Wirthmüller K, du Plessis A.A, Looijenga E.J.N, Topological Stability of Smooth Mappings, in: Lecture Notes in Math., vol. 552, Springer-Verlag, Berlin, 1976. Zbl0377.58006MR436203
  12. [12] Goresky M, MacPherson R, Stratified Morse Theory, in: Ergebnisse, vol. 14, Springer-Verlag, New York, 1988. Zbl0639.14012MR932724
  13. [13] Hattori A, Topology of Cn minus a finite number of affine hyperplanes in general position, J. Fac. Sci. Univ. Tokyo22 (1975) 205-219. Zbl0306.55011MR379883
  14. [14] Hillman J.A, Alexander Ideals of Links, in: Lecture Notes in Math., vol. 895, Springer-Verlag, Berlin, 1981. Zbl0491.57001MR653808
  15. [15] Jambu M, Papadima S, A generalization of fiber-type arrangements and a new deformation method, Topology37 (1998) 1135-1164. Zbl0988.52031MR1632975
  16. [16] Jambu M, Papadima S, Deformations of hypersolvable arrangements, Topology Appl.118 (2002) 103-111. Zbl0995.32017MR1877718
  17. [17] Libgober A, On the homotopy type of the complement to plane algebraic curves, J. Reine Angew. Math.397 (1986) 103-114. Zbl0576.14019MR839126
  18. [18] Libgober A, Homotopy groups of the complements to singular hypersurfaces II, Ann. Math.139 (1994) 117-144. Zbl0815.57017MR1259366
  19. [19] Mac Lane S, Homology, in: Grundlehren, vol. 114, Springer-Verlag, Berlin, 1963. Zbl0328.18009MR349792
  20. [20] Orlik P, Solomon L, Combinatorics and topology of complements of hyperplanes, Invent. Math.56 (1980) 167-189. Zbl0432.14016MR558866
  21. [21] Orlik P, Terao H, Arrangements of Hyperplanes, in: Grundlehren, vol. 300, Springer-Verlag, Berlin, 1992. Zbl0757.55001MR1217488
  22. [22] Papadima S, Suciu A, Higher homotopy groups of complements of complex hyperplane arrangements, Adv. Math.165 (2002) 71-100. Zbl1019.52016MR1880322
  23. [23] Randell R, Morse theory, Milnor fibers and minimality of hyperplane arrangements, Proc. Amer. Math. Soc.130 (2002) 2737-2743. Zbl1004.32010MR1900880
  24. [24] Rybnikov G, On the fundamental group of the complement of a complex hyperplane arrangement, available at , math.AG/9805056, DIMACS Tech. Report94-13 (1994) 33-50. 
  25. [25] Schechtman V, Terao H, Varchenko A, Local systems over complements of hyperplanes and the Kac–Kazhdan condition for singular vectors, J. Pure Appl. Algebra100 (1995) 93-102. Zbl0849.32025MR1344845
  26. [26] Whitehead G.W, Elements of Homotopy Theory, in: Grad. Texts in Math., vol. 61, Springer-Verlag, New York, 1978. Zbl0406.55001MR516508

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