Loop spaces of configuration spaces,braid-like groups, and knots

1. J. W. Alexander, A lemma on systems of knotted curves, Proc. Nat. Acad. Science USA 9 (1923), 93–95.

   Article  Google Scholar 

2. E. Artin, The theory of braids, Ann. of Math. 48 (1947), 101–126.

   Article  MathSciNet  MATH  Google Scholar 

3. D. Bar Natan, On the Vassiliev invariants, Topology 34 (1995), 423–472.

   Article  MathSciNet  MATH  Google Scholar 

4. J. Birman, Braids, Links, and Mapping Class Groups, Ann. of Math. Studies 66 (1971).

   Google Scholar 

5. A. K. Bousfield, and D. M. Kan, Homotopy Limits, Completions and Localizations, Lecture Notes in Math. 304, Springer-Verlag (1972).

   Book  MATH  Google Scholar 

6. F. R. Cohen, The homology of C_n+1-spaces, Lecture Notes in Math. 533, Springer-Verlag (1976), 207–351.

   Google Scholar 

7. F. R. Cohen, S. Gitler, On loop spaces of configuration spaces, preprint.

   Google Scholar 

8. F. R. Cohen, J. C. Moore, and J. A. Neisendorfer, The double suspension and exponents of the homotopy groups of spheres, Ann. of Math. 110 (1979), 549–565.

   Article  MathSciNet  MATH  Google Scholar 

9. F. R. Cohen, T. Sato, On the group of homotopy groups, student topology seminar, Univ. of Rochester, Spring 1998, preprint.

   Google Scholar 

10. F. R. Cohen, L. R. Taylor, On the representation theory associated to the cohomology of configuration spaces, Contemp. Math. 146 (1993), 91–109.

    MathSciNet  Google Scholar 

11. E. Fadell and S. Husseini, Geometry and Topology of Configuration Spaces, in preparation.

    Google Scholar 

12. E. Fadell and S. Husseini, The space of loops on configuration spaces and the Majer-Terracini index, Topological Methods in Nonlinear Analysis, Journal of the Julius Schauder Center (1996).

    Google Scholar 

13. E. Fadell, and L. Neuwirth, Configuration Spaces, Math. Scand. 10 (1962), 111–118.

    MathSciNet  MATH  Google Scholar 

14. M. Falk, and R. Randell, The lower central series of a fiber-type arrangement, Invent. Math. 82 (1985), 77–88.

    MathSciNet  MATH  Google Scholar 

15. T. G. Goodwillie, Cyclic homology, derivations, and Hochschild homology, Topology 24 (1985), 187–215.

    Article  MathSciNet  MATH  Google Scholar 

16. R. Hain, Infinitesimal presentations of the Torelli group, J. Amer. Math. Soc. 10 (1997), 597–691.

    Article  MathSciNet  MATH  Google Scholar 

17. I. M. James, Stiefel Manifolds, London Mathematical Society Lecture Note Series 78 (1965).

    Google Scholar 

18. T. Kohno, Linear represenations of braid groups and classical Yang—Baxter equations, Contemp. Math. 78 (1988), 339–363.

    Article  MathSciNet  Google Scholar 

19. T. Kohno, Vassiliev invariants and de Rham complex on the space of knots, Contemp. Math. 179 (1994), 123–138.

    Article  MathSciNet  Google Scholar 

20. M. Kontsevich, Vassiliev’s knot invariants, Advances in Soviet Mathematics 16 (1993), 137–150.

    MathSciNet  Google Scholar 

21. J.-L. Loday, Cyclic Homology, Grundlehren der mathematischen Wissenschaften 301 (1992), Springer-Verlag, Berlin.

    Google Scholar 

22. W. Magnus, A. Karrass, D. Solitar, Combinatorial Group Theory (1976), Dover.

    Google Scholar 

23. J. W. Milnor, and J. C. Moore, On the structure of Hopf algebras, Ann. of Math. 81 (1965), 211–264.

    Article  MathSciNet  MATH  Google Scholar 

24. T. Sato, On free groups and morphisms of coalgebras, student topology seminar, Univ. of Rochester, Spring 1998, preprint.

    Google Scholar 

25. P. S. Selick, 2-primary exponents for the homotopy groups of spheres, Topology 23 (1984), 97–99.

    Article  MathSciNet  MATH  Google Scholar 

26. V. Vassiliev, Cohomology of knot spaces, Theory of singularities and its applications, Amer. Math. Soc. (1992).

    Google Scholar 

27. M. Xicoténcatl, Orbit configuration spaces, Thesis, Univ. of Rochester, Spring 1996.

    Google Scholar 

Download references