The -invariants for groups

Author:
M. A. Gutiérrez

Journal:
Proc. Amer. Math. Soc. **55** (1976), 293-298

MSC:
Primary 16A26; Secondary 55A25

MathSciNet review:
0422328

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Abstract: Given a presentation for a group , the cobar differentials are invariants of . These invariants can be interpreted to be the Massey coproducts of , and, if is the Wirtinger presentation of a link group, they coincide with the -invariants of Milnor.

**[1]**F. Bachman and L. Grunenfelder,*The periodicity in the graded ring associated with an integral grouping*(to appear).**[2]**Ralph H. Fox,*Free differential calculus. I. Derivation in the free group ring*, Ann. of Math. (2)**57**(1953), 547–560. MR**0053938****[3]**M. Gutierrez,*The cobar construction and applications to groups*(to appear).**[4]**Wilhelm Magnus, Abraham Karrass, and Donald Solitar,*Combinatorial group theory: Presentations of groups in terms of generators and relations*, Interscience Publishers [John Wiley & Sons, Inc.], New York-London-Sydney, 1966. MR**0207802****[5]**John Milnor,*Isotopy of links. Algebraic geometry and topology*, A symposium in honor of S. Lefschetz, Princeton University Press, Princeton, N. J., 1957, pp. 280–306. MR**0092150****[6]**I. B. S. Passi,*Polynomial maps on groups*, J. Algebra**9**(1968), 121–151. MR**0231915****[7]**J. Stallings,*The cobar construction and the fundamental ideal*, Lecture given at Fox Colloquium in Fine Hall, March, 1973.**[8]**H. F. Trotter,*Homology of group systems with applications to knot theory*, Ann. of Math. (2)**76**(1962), 464–498. MR**0143201**

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DOI:
http://dx.doi.org/10.1090/S0002-9939-1976-0422328-8

Keywords:
Cobar construction,
Fox derivative,
- invariants

Article copyright:
© Copyright 1976
American Mathematical Society