We determine the center of a meta-nilpotent quotient of a mapping-torus group. As a corollary, we introduce two invariants, which are quadratic forms, of knots and of mapping classes.
References
J. Hillman: Algebraic Invariants of Links, Second edition, Series on Knots and Everything 52, World Scientific Publishing Co. Pte. Ltd., Hackensack, NJ, 2012.J. Hillman: Algebraic Invariants of Links, Second edition, Series on Knots and Everything 52, World Scientific Publishing Co. Pte. Ltd., Hackensack, NJ, 2012.
T. Kitano: Johnson's homomorphisms of subgroups of the mapping class group, the Magnus expansion and Massey higher products of mapping tori, Topology Appl. 69 (1996), 165-172.T. Kitano: Johnson's homomorphisms of subgroups of the mapping class group, the Magnus expansion and Massey higher products of mapping tori, Topology Appl. 69 (1996), 165-172.
D. Johnson: A survey of the Torelli group; in Low-dimensional topology (San Francisco, Calif., 1891), Contemporary Mathematics 20, 165-179, Amer. Math. Soc., Providence, RI, 1983.D. Johnson: A survey of the Torelli group; in Low-dimensional topology (San Francisco, Calif., 1891), Contemporary Mathematics 20, 165-179, Amer. Math. Soc., Providence, RI, 1983.
T. Satoh: A survey of the Johnson homomorphisms of the automorphism groups of free groups and related topics; in Handbook of Teichmueller theory, volume V. (Editor: A. Papadopoulos), 167-209.T. Satoh: A survey of the Johnson homomorphisms of the automorphism groups of free groups and related topics; in Handbook of Teichmueller theory, volume V. (Editor: A. Papadopoulos), 167-209.