1. Preliminaries. In [ l ] the structure of the weakly complex bordism of 1 connected semisimple Lie groups was studied via the Milnor, Eilenberg-Moore, Rothenberg-Steenrod sequence. See [l] for notation. In this paper we amplify the Adams spectral sequence [2], [3], [4] and relate this tool to the weakly complex cobordism theory. The techniques apply to any finite CW complex. In particular we ...

The spectral sequence (1) was introduced in [9] and [8]. Here, BPR is the Realoriented Brown-Peterson spectrum, which was constructed from Landweber’s Real cobordism spectrum MR [10] by Araki [2]. These are Z/2-equivariant spectra, indexed on RO(Z/2). The subscript ⋆ refers to the RO(Z/2)-indexing, i. e. all (bi)degrees k + lα, k, l ∈ Z, where α is the sign representation of Z/2. Thus, the spec...

We consider self-adjoint unbounded Jacobi matrices with diagonal qn = n and weights λn = cnn, where cn is a 2-periodical sequence of real numbers. The parameter space is decomposed into several separate regions, where the spectrum is either purely absolutely continuous or discrete. This constitutes an example of the spectral phase transition of the first order. We study the lines where the spec...

Let p:E B be a fibration over a connected space B with fiber F. The Eilenberg-Moore spectral sequence of p is a second quadrant spectral sequence which tries and sometimes fails to converge strongly to the homology of F (see 1-53). The purpose of this paper is to determine what the spectral sequence does converge to. An abstract answer (Theorem 1.1) is that the spectral sequence almost always c...

There are p-local spectra T (m) with BP∗(T (m)) = BP∗[t1, . . . , tm]. In this paper we determine the first nontrivial differential in the Adams– Novikov spectral sequence for each of them for p odd. For m = 0 (the sphere spectrum) this is the Toda differential, whose source has filtration 2 and whose target is the first nontrivial element in filtration 2p + 1. The same goes for m = 1, and for ...

Mahowald proved the height 1 telescope conjecture at prime 2 as an application of his seminal work on bo-resolutions. In this paper we study through lens tmf-resolutions. To end compute structure tmf-resolution for a specifc type complex Z. We find that, analogous to case, E1-page possesses decomposition into v2-periodic summand, and Eilenberg-MacLane summand which consists bounded v2-torsion. ...

We discuss the first author's Picard groups of stable homo-topy. We give s. detailed description of the calculation of PiC!, and go onto describe geometric constructions for lifts of the elements of Pic!. Wealso construct a 15 cell complex that localizeil to what we speculate is aninteresting element ofPk2 •For all n we describe an algebraic approxllna-tion to Picn u...

In [1], Miller, Ravenel and Wilson defined generalized beta elements in the E2-term of the Adams-Novikov spectral sequence converging to the stable homotopy groups of spheres, and in [5], Oka showed that the beta elements of the form βtp2/r for positive integers t and r survives to the stable homotopy groups at a prime p > 3, when r ≤ 2p − 2 and r ≤ 2p if t > 1. In this paper, we expand the con...