In this paper, some groups Ext A (Zp, Zp) with specialized s and t are first computed by the May spectral sequence. Then we make use of the Adams spectral sequence to prove the existence of a new nontrivial family of filtration s+5 in the stable homotopy groups of spheres πpnq+(s+3)pq+(s+1)q−5S which is represented (up to a nonzero scalar) by β̃s+2b0hn ∈ Ext q+(s+3)pq+(s+1)q+s A (Zp, Zp) in the ...

We present some data on the cohomology of the motivic Steenrod algebra over an algebraically closed field of characteristic 0. Our results are based on computer calculations and a motivic version of the May spectral sequence. We discuss features of the associated Adams spectral sequence, and use these tools to give new proofs of some results in classical algebraic topology. We also consider a m...

Let p be an odd prime and A be the mod p Steenrod algebra. For computing the stable homotopy groups of spheres with the classical Adams spectral sequence, we must compute the E2 -term of the Adams spectral sequence, Ext A ( p, p) . In this paper we prove that in the cohomology of A , the product k0hnδ̃s+4 ∈ Ext s+7,t(s,n)+s A ( p, p) , is nontrivial for n ≥ 5, and trivial for n = 3, 4, where δ̃s+...

ALICEROBBIN ABSTRACT THISARTICLE EXAMINES SELECTED ECONOMIC and social indicators of our multiracial and multiethnic society at the end of the twentieth century to provide an information base for wise decisions about effective library services. The statistical profile describes the demography, economic well-being , and educational attainment of the principal racial and Hispanic origin groups. T...

This is primarily an essay on the Serre spectral sequence for the homology/cohomology of a fibration. But we view the Serre spectral sequence as a special case of the spectral sequence of a filtered space or filtered chain complex, which has many other important cases: the spectral sequence(s) of a double complex (Grothendieck’s composite functor spectral sequence in homological algebra is obta...

We want to thank the authors for responding to our paper and for apprising readers as to the effects of the new information technologies in Asian educational settings. We think Miyake has characterized our argument very accurately and succinctly. As she points out the equity issues we raise are exacerbated in Asia because the resources available through new technologies are mostly in English. B...

S Balasegaram, J M Watson, A M C Rose, A Charlett, A J Nunn, A Rushdy, J Leese, L P Ormerod, on behalf of the Public Health Laboratory Service/British Thoracic Society/Department of Health Collaborative Group . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ...

1. Exact couples and spectral sequences 2 1.1. Spectral sequences 2 1.2. Exact couples 2 1.3. The spectral sequence associated to an exact couple 3 1.4. Example: the spectral sequence of a filtered space 3 References 4 2. Pages of the spectral sequence 4 2.1. Iterated subquotients 4 2.2. Formula for the rth page 5 2.3. Filtered spaces 6 3. Convergence 6 3.1. Simplest case: first quadrant spectr...

We introduce a variant of the slice spectral sequence which uses only regular slice cells, and state the precise relationship between the two spectral sequences. We analyze how the slice filtration of an equivariant spectrum that is concentrated over a normal subgroup is related to the slice filtration of its geometric fixed points, and use this to prove a conjecture of Hill on the slice filtra...