On the cohomology of Seifert and graph manifolds. (English) Zbl 1022.57013
The authors describe a cell-decomposition of a general Seifert manifold \(M^3= SF(g,b,r:(\alpha_1,\beta_1),\dots,(\alpha_r,\beta_r))\). They construct chain and cochain complexes from the resulting CW-complex, and calculate the cohomology ring of \(M^3\).
A corresponding calculation is made for a graph manifold which is constructed, roughly speaking, from the union of a finite number of Seifert manifolds which intersect one another along their boundary tori.
A corresponding calculation is made for a graph manifold which is constructed, roughly speaking, from the union of a finite number of Seifert manifolds which intersect one another along their boundary tori.
Reviewer: Lee P.Neuwirth (Princeton)
MSC:
| 57N65 | Algebraic topology of manifolds |
| 55R99 | Fiber spaces and bundles in algebraic topology |
| 57M50 | General geometric structures on low-dimensional manifolds |
| 55N99 | Homology and cohomology theories in algebraic topology |
| 57N10 | Topology of general \(3\)-manifolds (MSC2010) |
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