On May spectral sequences
نویسندگان
چکیده
منابع مشابه
Notes on Spectral Sequences
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...
متن کاملNotes on Spectral Sequences
making the triangle exact at each vertex. Given this, the homomorphism d = jk : E → E satisfies dd = jkjk = 0 since kj = 0 The derived couple of (A,E, i, j, k) is (A′, E ′, i′, j′, k′), where E ′ = Ker(d)/Im(d), A′ = iA, i′(a) = ia, j′(ia) = [ja], k′[e] = ke. To see that j′ is well defined, suppose ia = ib: then exactness implies that b = a+ ke for some e ∈ E, and then [jb] = [ja] + [jke] = [ja...
متن کاملNotes on Spectral Sequences
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...
متن کاملAn essay on spectral sequences
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...
متن کاملSpectral Sequences
Let E pq be the vertical homology Hg(E 0 p∗) of this complex. In other words, if Z pq = ker(d v pq), B pq = im(d v p,q+1), then E pq = Z 1 pq/B 1 pq. We note that d h induces maps E pq → E p−1,q as follows. The condition dd = −dd shows that d(Z pq) ⊆ Z p−1,q and d(B pq) ⊆ B p−1,q; therefore, there is a homomorphism d̃pq : E 1 pq → E p−1,q. Let E pq be the horizontal homology Hp(E ∗q) of this com...
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ژورنال
عنوان ژورنال: Kyoto Journal of Mathematics
سال: 1997
ISSN: 2156-2261
DOI: 10.1215/kjm/1250518403