Geometry & Topology Volume 8, issue 3 (2004)

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Homotopy Lie algebras, lower central series and the Koszul property

Ştefan Papadima and Alexander I Suciu

Geometry & Topology 8 (2004) 1079–1125

DOI: 10.2140/gt.2004.8.1079

Bibliography

1	D J Anick, Connections between Yoneda and Pontrjagin algebras, from: "Algebraic topology, Aarhus 1982 (Aarhus, 1982)", Lecture Notes in Math. 1051, Springer (1984) 331 MR764587
2	H J Baues, Commutator calculus and groups of homotopy classes, London Mathematical Society Lecture Note Series 50, Cambridge University Press (1981) MR634675
3	A Beilinson, V Ginzburg, W Soergel, Koszul duality patterns in representation theory, J. Amer. Math. Soc. 9 (1996) 473 MR1322847
4	A K Bousfield, V K A M Gugenheim, On $\mathrm{PL}$ de Rham theory and rational homotopy type, Mem. Amer. Math. Soc. 8 (1976) MR0425956
5	B Berceanu, Ş Papadima, Cohomologically generic 2–complexes and 3–dimensional Poincaré complexes, Math. Ann. 298 (1994) 457 MR1262770
6	R Bott, H Samelson, On the Pontryagin product in spaces of paths, Comment. Math. Helv. 27 (1953) MR0060233
7	E Brieskorn, Sur les groupes de tresses [d'après V I: Arnol' d], from: "Séminaire Bourbaki, 24ème année (1971/1972), Exp. No. 401", Springer (1973) MR0422674
8	D C Cohen, F R Cohen, M Xicoténcatl, Lie algebras associated to fiber-type arrangements, Int. Math. Res. Not. (2003) 1591 MR1979686
9	F R Cohen, S Gitler, Loop spaces of configuration spaces, braid-like groups, and knots, from: "Cohomological methods in homotopy theory (Bellaterra, 1998)", Progr. Math. 196, Birkhäuser (2001) 59 MR1851248
10	F R Cohen, S Gitler, On loop spaces of configuration spaces, Trans. Amer. Math. Soc. 354 (2002) 1705 MR1881013
11	F R Cohen, T Kohno, M Xicoténcatl, Orbit configuration spaces associated to discrete subgroups of $\mathrm{PSL}(2,\mathbb{R})$ arXiv:math.AT/0310393
12	F R Cohen, T Sato, On groups of homotopy groups, loop spaces and braid-like groups, preprint (2001)
13	F R Cohen, M A Xicoténcatl, On orbit configuration spaces associated to the Gaussian integers: homotopy and homology groups, Topology Appl. 118 (2002) 17 MR1877713
14	C De Concini, C Procesi, Wonderful models of subspace arrangements, Selecta Math. $($N.S.$)$ 1 (1995) 459 MR1366622
15	P Deligne, P Griffiths, J Morgan, D Sullivan, Real homotopy theory of Kähler manifolds, Invent. Math. 29 (1975) 245 MR0382702
16	E R Fadell, S Y Husseini, Geometry and topology of configuration spaces, Springer Monographs in Mathematics, Springer (2001) MR1802644
17	M Falk, R Randell, The lower central series of a fiber-type arrangement, Invent. Math. 82 (1985) 77 MR808110
18	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 MR0379883
19	P Hilton, G Mislin, J Roitberg, Localization of nilpotent groups and spaces, North-Holland Mathematics Studies 15, North-Holland Publishing Co. (1975) MR0478146
20	M Jambu, S Papadima, A generalization of fiber-type arrangements and a new deformation method, Topology 37 (1998) 1135 MR1632975
21	M A Kervaire, An interpretation of G. Whitehead's generalization of H. Hopf's invariant, Ann. of Math. $(2)$ 69 (1959) 345 MR0102809
22	T Kohno, Série de Poincaré–Koszul associée aux groupes de tresses pures, Invent. Math. 82 (1985) 57 MR808109
23	U Koschorke, D Rolfsen, Higher-dimensional link operations and stable homotopy, Pacific J. Math. 139 (1989) 87 MR1010788
24	J P Labute, On the descending central series of groups with a single defining relation, J. Algebra 14 (1970) 16 MR0251111
25	M Lazard, Sur les groupes nilpotents et les anneaux de Lie, Ann. Sci. Ecole Norm. Sup. $(3)$ 71 (1954) 101 MR0088496
26	M Markl, Ş Papadima, Homotopy Lie algebras and fundamental groups via deformation theory, Ann. Inst. Fourier (Grenoble) 42 (1992) 905 MR1196099
27	J Milnor, Morse theory, Annals of Mathematics Studies 51, Princeton University Press (1963) MR0163331
28	J W Milnor, J C Moore, On the structure of Hopf algebras, Ann. of Math. $(2)$ 81 (1965) 211 MR0174052
29	J Neisendorfer, T Miller, Formal and coformal spaces, Illinois J. Math. 22 (1978) 565 MR0500938
30	A Némethi, The link of the sum of two holomorphic functions, from: "Proceedings of the National Conference on Geometry and Topology (Romanian) (Tîrgovişte, 1986)", Univ. Bucureşti, Bucharest (1988) 181 MR980018
31	M Oka, On the fundamental group of the complement of certain plane curves, J. Math. Soc. Japan 30 (1978) 579 MR513071
32	Ş Papadima, The cellular structure of formal homotopy types, J. Pure Appl. Algebra 35 (1985) 171 MR775469
33	S Papadima, Campbell–Hausdorff invariants of links, Proc. London Math. Soc. $(3)$ 75 (1997) 641 MR1466664
34	S Papadima, Braid commutators and homogenous Campbell–Hausdorff tests, Pacific J. Math. 197 (2001) 383 MR1815262
35	S Papadima, A I Suciu, Rational homotopy groups and Koszul algebras, C. R. Math. Acad. Sci. Paris 335 (2002) 53 MR1920995
36	S Papadima, A I Suciu, Chen Lie algebras, Int. Math. Res. Not. (2004) 1057 MR2037049
37	S Papadima, S Yuzvinsky, On rational $K[\pi,1]$ spaces and Koszul algebras, J. Pure Appl. Algebra 144 (1999) 157 MR1731434
38	G J Porter, Higher-order Whitehead products, Topology 3 (1965) 123 MR0174054
39	S B Priddy, Koszul resolutions, Trans. Amer. Math. Soc. 152 (1970) 39 MR0265437
40	D Quillen, Rational homotopy theory, Ann. of Math. $(2)$ 90 (1969) 205 MR0258031
41	D Rolfsen, Knots and links, Mathematics Lecture Series 7, Publish or Perish (1976) MR0515288
42	J E Roos, On the characterisation of Koszul algebras. Four counterexamples, C. R. Acad. Sci. Paris Sér. I Math. 321 (1995) 15 MR1340075
43	T Sato, On the group of morphisms of coalgebras, PhD thesis, University of Rochester, New York (2000)
44	H Scheerer, On rationalized $H$– and co-$H$–spaces. With an appendix on decomposable $H$– and co-$H$–spaces, Manuscripta Math. 51 (1985) 63 MR788673
45	H K Schenck, A I Suciu, Lower central series and free resolutions of hyperplane arrangements, Trans. Amer. Math. Soc. 354 (2002) 3409 MR1911506
46	J P Serre, Lie algebras and Lie groups, Lecture Notes in Mathematics 1500, Springer (1992) MR1176100
47	B Shelton, S Yuzvinsky, Koszul algebras from graphs and hyperplane arrangements, J. London Math. Soc. $(2)$ 56 (1997) 477 MR1610447
48	H Shiga, N Yagita, Graded algebras having a unique rational homotopy type, Proc. Amer. Math. Soc. 85 (1982) 623 MR660618
49	T Stanford, Braid commutators and Vassiliev invariants, Pacific J. Math. 174 (1996) 269 MR1398378
50	D Sullivan, Infinitesimal computations in topology, Inst. Hautes Études Sci. Publ. Math. (1977) MR0646078
51	D Tanré, Homotopie rationnelle: modèles de Chen, Quillen, Sullivan, Lecture Notes in Mathematics 1025, Springer (1983) MR764769
52	G W Whitehead, Elements of homotopy theory, Graduate Texts in Mathematics 61, Springer (1978) MR516508
53	S Yuzvinskiĭ, Orlik–Solomon algebras in algebra and topology, Uspekhi Mat. Nauk 56 (2001) 87 MR1859708
54	S Yuzvinsky, Small rational model of subspace complement, Trans. Amer. Math. Soc. 354 (2002) 1921 MR1881024