Skip to main content
×
Home
    • Aa
    • Aa

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

  • Tim. D. Cochran (a1)
Abstract

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.

Copyright
Linked references
Hide All

This list contains references from the content that can be linked to their source. For a full set of references and notes please see the PDF or HTML where available.

[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.

Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

Mathematical Proceedings of the Cambridge Philosophical Society
  • ISSN: 0305-0041
  • EISSN: 1469-8064
  • URL: /core/journals/mathematical-proceedings-of-the-cambridge-philosophical-society
Please enter your name
Please enter a valid email address
Who would you like to send this to? *
×

Metrics

Full text views

Total number of HTML views: 0
Total number of PDF views: 5 *
Loading metrics...

Abstract views

Total abstract views: 84 *
Loading metrics...

* Views captured on Cambridge Core between September 2016 - 29th May 2017. This data will be updated every 24 hours.