and Magnus described generators for the kernel of the canonical epimorphism from the automorphism group of F n to the general linear group over the integers. In particular among them are the automorphisms χ k,i which conjugate the generator x k by the generator x i leaving the x j fixed for j = k. A computation of the cohomology ring as well as the Lie… (More)
We determine a set of generators for the Brunnian braids on a general surface M for M = S 2 or RP 2. For the case M = S 2 or RP 2 , a set of generators for the Brunnian braids on M is given by our generating set together with the homotopy groups of a 2-sphere.
The maps from loop suspensions to loop spaces are investigated using group representations in this article. The shuffle relations on the Cohen groups are given. By using these relations, a universal ring for functorial self maps of double loop spaces of double suspensions is given. Moreover the obstructions to the classical exponent problem in homotopy… (More)
In this paper, we investigate some applications of commutator subgroups to homotopy groups and geometric groups. In particular, we show that the intersection subgroups of some canonical subgroups in certain link groups modulo their symmetric commutator subgroups are isomorphic to the (higher) homotopy groups. This gives a connection between links and… (More)
In this article, we investigate the functors from modules to modules that occur as the summands of tensor powers and the functors from modules to Hopf algebras that occur as natural coalgebra summands of tensor algebras. The main results provide some explicit natural coalgebra summands of tensor algebras. As a consequence, we obtain some decompositions of… (More)
In this paper we continue our study of the Delta-group structure on the braid groups and mapping class groups of a surface. We calculate the homotopy groups of these Delta-groups and prove some results about Brunnian braid groups and Brunnian mapping class groups. This is the second of a pair of papers on these structures.
For spaces localized at 2, the classical EHP fibrations [1, 13]
We prove two homotopy decomposition theorems for the loops on simply-connected co-H-spaces, including a generalization of the Hilton-Milnor Theorem. Several examples are given.
We prove two homotopy decomposition theorems for the loops on co-H-spaces, including a generalization of the Hilton-Milnor Theorem. These are applied to problems arising in algebra, representation theory, toric topol-ogy, and the study of quasi-symmetric functions.
In this paper, we investigated the existence of subnormal solution and the growth properties of solutions for nth order periodic coefficient homogeneous linear differential equations… (More)