We introduce a new spectral sequence called the p-chain spectral sequence which converges to the (co-)homology of a contravariant C-space with coefficients in a covariant C-spectrum for a small category C. It is different from the corresponding Atiyah–Hirzebruch-type spectral sequence. It can be used in combination with the Isomorphism Conjectures of Baum and Connes and Farrell and Jones to com...

     Data reduction is used to aggregate or amalgamate the large data sets into smaller and manageable information pieces in order to fast and accurate classification of different attributes. However, excessive spatial or spectral data reduction may result in losing or masking important radiometric information. Therefore, we conducted this research to evaluate the effectiveness of the different...

1. Local coefficient systems 2 1.1. The fundamental groupoid 2 1.2. Coefficient systems 3 1.3. Path connected based spaces 4 1.4. Singular chains with local coefficients 4 1.5. Homology with local coefficients 5 1.6. Universal covers 7 2. Exact couples and spectral sequences 9 2.1. Spectral sequences 9 2.2. Exact couples 9 2.3. The spectral sequence associated to an exact couple 10 2.4. Example...

The $E_2$ term of the Adams spectral sequence may be identified with certain derived functors, and this also holds for a number other sequences. Our goal is to show how higher terms such sequences are determined by truncations relative defined in simplicial functors called mapping algebras

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Let A be the mod p Steenrod algebra and S the sphere spectrum localized at p, where p is an odd prime. In 2001 Lin detected a new family in the stable homotopy of spheres which is represented by (b0hn − h1bn−1) ∈ Ext n+p)q A (Zp,Zp) in the Adams spectral sequence. At the same time, he proved that i∗(h1hn) ∈ Ext +p)q A (H ∗M,Zp) is a permanent cycle in the Adams spectral sequence and converges t...

When X is an associative H-space, the bar spectral sequence computes the homology of the delooping, H∗(BX). If X is an n-fold loop space for n ≥ 2 this is a spectral sequence of Hopf algebras. Using machinery by Sugawara and Clark, we show that the spectral sequence filtration respects the Browder bracket structure on H∗(BX), and so it is moreover a spectral sequence of Poisson algebras. Throug...