Chen Lie algebras

International Mathematics Research Notices

Volumn , Issue 21, 2004, Pages 1057-1086

  Papadima, Stefan ^a   Suciu, Alexander I ^b  

^a ACADEMY OF ROMANIAN SCIENTISTS   (Romania)

^b NORTHEASTERN UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 2942674900     PISSN: 10737928     EISSN: None     Source Type: Journal    
DOI: 10.1155/s1073792804132017     Document Type: Article

References (42)

1. D. J. Anick, Inert sets and the Lie algebra associated to a group, J. Algebra 111 (1987), no. 1, 154-165.
2. B. Berceanu and Ş. Papadima, Cohomologically generic 2-complexes and 3-dimensional Poincaré complexes, Math. Ann. 298 (1994), no. 3, 457-480.
3. _, Moduli spaces for generic low-dimensional complexes, J. Pure Appl. Algebra 95 (1994), no. 1, 1-25.
4. N. Bourbaki, Groupes et Algèbres de Lie, Hermann, Paris, 1972.
5. E. Brieskorn, Sur les groupes de tresses [d'après V. I. Arnol'd], Séminaire Bourbaki, 24ème année (1971/1972), Exp. No. 401, Lecture Notes in Math., vol. 317, Springer-Verlag, Berlin, 1973, pp. 21-44.
6. K. T. Chen, Integration in free groups, Ann. of Math. (2) 54 (1951), 147-162.
7. _, Commutator calculus and link invariants, Proc. Amer. Math. Soc. 3 (1952), 44-55.
8. 1, Adv. Math. 23 (1977), no. 2, 181-210.
9. D. C. Cohen and A. I. Suciu, The Chen groups of the pure braid group, The Čech Centennial (Boston, Mass, 1993), Contemp. Math., vol. 181, American Mathematical Society, Rhode Island, 1995, pp. 45-64.
10. _, Alexander invariants of complex hyperplane arrangements, Trans. Amer. Math. Soc. 351 (1999), no. 10, 4043-4067.
11. _, Characteristic varieties of arrangements, Math. Proc. Cambridge Philos. Soc. 127 (1999), no. 1, 33-53.
12. P. Deligne, P. Griffiths, J. Morgan, and D. Sullivan, Real homotopy theory of Kähler manifolds, Invent. Math. 29 (1975), no. 3, 245-274.
13. M. Falk and R. Randell, The lower central series of a fiber-type arrangement, Invent. Math. 82 (1985), no. 1, 77-88.
14. R. H. Fox, Free differential calculus. I. Derivation in the free group ring, Ann. of Math. (2) 57 (1953), 547-560.
15. D. R. Grayson and M. E. Stillman, Macaulay 2: a software system for research in algebraic geometry, http://www.math.uiuc.edu/Macaulay2.
16. R. M. Hain, Iterated integrals, intersection theory and link groups, Topology 24 (1985), no. 1, 45-66, erratum: Topology 25 (1986), no. 4, 585-586.
17. P. Hilton, G. Mislin, and J. Roitberg, Localization of Nilpotent Groups and Spaces, North-Holland Mathematics Studies, no. 15, North-Holland Publishing, Amsterdam, 1975.
18. M. Jambu and Ş. Papadima, A generalization of fiber-type arrangements and a new deformation method, Topology 37 (1998), no. 6, 1135-1164.
19. T. Kohno, On the holonomy Lie algebra and the nilpotent completion of the fundamental group of the complement of hypersurfaces, Nagoya Math. J. 92 (1983), 21-37.
20. _, Série de Poincaré-Koszul associée aux groupes de tresses pures [The Poincaré-Koszul series associated with pure braid groups], Invent. Math. 82 (1985), no. 1, 57-75 (French).
21. S. Kojima, Nilpotent completions and Lie rings associated to link groups, Comment. Math. Helv.58 (1983), no. 1, 115-134.
22. J. P. Labute, On the descending central series of groups with a single defining relation, J. Algebra 14 (1970), 16-23.
23. _, The Lie algebra associated to the lower central series of a link group and Murasugi's conjecture, Proc. Amer. Math. Soc. 109 (1990), no. 4, 951-956.
24. M. Lazard, Sur les groupes nilpotents et les anneaux de Lie, Ann. Sci. École Norm. Sup. (3) 71 (1954), 101-190 (French).
25. T. Maeda, Lower central series of link groups, Ph.D. thesis, University of Toronto, Ontario, 1983.
26. W. Magnus, A. Karrass, and D. Solitar, Combinatorial Group Theory, 2nd ed., Dover Publications, New York, 1976.
27. M. Markl and Ş. Papadima, Homotopy Lie algebras and fundamental groups via deformation theory, Ann. Inst. Fourier (Grenoble) 42 (1992), no. 4, 905-935.
28. W. S. Massey, Completion of link modules, Duke Math. J. 47 (1980), no. 2, 399-420.
29. W. S. Massey and L. Traldi, On a conjecture of K. Murasugi, Pacific J. Math. 124 (1986), no. 1, 193-213.
30. D. Matei and A. I. Suciu, Cohomology rings and nilpotent quotients of real and complex arrangements, Arrangements-Tokyo 1998, Adv. Stud. Pure Math., vol. 27, Kinokuniya, Tokyo, 2000, pp. 185-215.
31. J. W. Morgan, The algebraic topology of smooth algebraic varieties, Inst. Hautes Études Sci. Publ. Math. (1978), no. 48, 137-204.
32. K. Murasugi, On Milnor's invariant for links. II. The Chen group, Trans. Amer. Math. Soc. 148 (1970), 41-61.
33. P. Orlik and L. Solomon, Combinatorics and topology of complements of hyperplanes, Invent. Math. 56 (1980), no. 2, 167-189.
34. Ş. Papadima, Generalized ̄μ-invariants for links and hyperplane arrangements, Proc. London Math. Soc. (3) 84 (2002), no. 2, 492-512.
35. Ş. Papadima and A. I. Suciu, When does the associated graded Lie algebra of an arrangement group decompose?, preprint, 2003, http://arXiv.org/abs/math.CO/0309324.
36. Ş. Papadima and S. Yuzvinsky, On rational K[φ, 1] spaces and Koszul algebras, J. Pure Appl. Algebra 144 (1999), no. 2, 157-167.
37. D. G. Quillen, On the associated graded ring of a group ring, J. Algebra 10 (1968), 411-418.
38. _, Rational homotopy theory, Ann. of Math. (2) 90 (1969), 205-295.
39. H. K. Schenck and A. I. Suciu, Lower central series and free resolutions of hyperplane arrangements, Trans. Amer. Math. Soc. 354 (2002), no. 9, 3409-3433.
40. A. I. Suciu, Fundamental groups of line arrangements: enumerative aspects, Advances in Algebraic Geometry Motivated by Physics (Lowell, Mass, 2000), Contemp. Math., vol. 276, American Mathematical Society, Rhode Island, 2001, pp. 43-79.
41. D. Sullivan, Infinitesimal computations in topology, Inst. Hautes Études Sci. Publ. Math. (1977), no. 47, 269-331.
42. L. Traldi, Linking numbers and Chen groups, Topology Appl. 31 (1989), no. 1, 55-71.