PULLBACK CAT-1 RACKS

Abstract

In this paper we introduce the notion of pullbak cat-1 racks, which is obtained by a certain kind of pullback diagram in the category of racks.

Keywords

• Rack,crossed module,cat-1 rack,pullback

References

1. [1] M. Alp. Pullbacks of crossed modules and cat-1 groups. Turkish Journal of Mathematics, 22:273-281, 1998.
2. [2] E. Brieskorn. Automorphic sets and braids and singularities. Braids, AMS-IMS-SIAM Jt. Summer Res. Conf., Santa Cruz/Calif. 1986, Contemp. Math. 78, 45-115 (1988)., 1988.
3. [3] R. Brown and C.D. Wensley. On innite induced crossed modules and the homotopy 2-type of mapping cones. Theory Appl. Categ., 1, 1995.
4. [4] J.H. Conway and G. Wraith. Unpublished correspondence. 1959.
5. [5] A.S. Crans and F. Wagemann. Crossed modules of racks. Homology Homotopy Appl., 16(2):85-106, 2014.
6. [6] R. Fenn and C. Rourke. Racks and links in codimension two. J. Knot Theory Ramications, 1(4):343-406, 1992.
7. [7] L.H. KauFFman. Knots and Physics. K & E series on knots and everything. World Scientic, 2001.
8. [8] J.L. Loday. Spaces with nitely many non-trivial homotopy groups. Journal of Pure and Applied Algebra, 24(2):179-202, 1982.

9. [9] D. Stanovskiy. Left distributive left quasigroup, phd thesis, 2004.
10. [10] J.H.C. Whitehead. On adding relations to homotopy groups. Ann. Math. (2), 42:409-428, 1941.