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    MELIKHOV, SERGEY A. and REPOVŠ, DUŠAN 2005. n-QUASI-ISOTOPY I: QUESTIONS OF NILPOTENCE. Journal of Knot Theory and Its Ramifications, Vol. 14, Issue. 05, p. 571.

    Мелихов, Сергей Александрович Melikhov, Sergey Aleksandrovich Михайлов, Роман Валерьевич and Mikhailov, Roman Valer'evich 2001. Зацепления по модулю узлов и Проблема изотопической реализации. Успехи математических наук, Vol. 56, Issue. 2, p. 219.

  • Mathematical Proceedings of the Cambridge Philosophical Society, Volume 97, Issue 3
  • May 1985, pp. 465-472

A topological proof of Stallings' theorem on lower central series of groups

  • Tim. D. Cochran (a1)
  • DOI:
  • Published online: 24 October 2008

For a topologist, the fundamental group G of a space is usually the most important non-abelian algebraic object of study. However, under many equivalence relationships G is not invariant, so topologists have been led to examine other algebraic objects. In particular, for questions of concordance the lower central series of G seems to play the crucial role. Recall that the lower central series Gn(n = 1,2,...) of G is defined by G1 = G, Gn = [G, Gn_1] for n > 1, and the lower central sequence of G is the sequence of quotients G/Gn.

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[1]S. E. Cappell and J. Shaneson . Link cobordism. Comment. Math. Helv. 55 (1980), 2049.

[2]A. J. Casson . Link cobordism and Milnor's invariant. Bull. London Math. Soc. 7 (1975), 3940.

[3]T. D. Cochran . Slice links in S4. Trans. Amer. Math. Soc. 285 (1984), 398401.

[5]P. E. Conner and E. Floyd . Differentiable periodic maps. Bull. Amer. Math. Soc. 68 (1962), 7686.

[6]R. Demeo . Link cobordism. Duke Math. J. 48 (1981), 2333.

[9]S. Kojima . Milnor's µ̅-invariants, Massey products and Whitney's trick in 4-dimensions. Topology Appl. 16 (1983), 4360.

[11]K. Murasugi . On Milnor's invariant for links. Trans. Amer. Math. Soc. 124 (1966), 94110.

[12]R. Porter . Milnor's µ̅-invariants and Massey products. Trans. Amer. Math. Soc. 257 (1979), 3971.

[13]J. Stallings . Homology and central series of groups. J. Algebra 2 (1965), 170181.

[14]L. Traldi . Milnor's invariants and the completions of link modules. Trans. Amer. Math. Soc. 284 (1984), 401424.

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