Linking in tree-manifolds. (English) Zbl 1535.57043
Let \(T\) be a tree whose vertices are \(2m\)-dimensional oriented vector fields over the sphere \(S^{2m}\). Plumbing, as described in [W. Browder, Surgery on simply-connected manifolds. Berlin-Heidelberg-New York: Springer-Verlag (1972; Zbl 0239.57016)], gives an oriented manifold \(W(T)\) whose boundary \(M(T)\) is called a tree manifold. The fibers of the associated sphere bundles to the vertices of \(T\) provide embedded \((2m-1)\)-dimensional spheres in \(M(T)\). In the case when \(M(T)\) is a rational homology sphere, the author calculates the linking number of these spheres. This paper corrects earlier work of T. tom Dieck [Geom. Dedicata 34, No. 1, 57–65 (1990; Zbl 0759.57016)].
Reviewer: James Hebda (St. Louis)
MSC:
| 57R19 | Algebraic topology on manifolds and differential topology |
| 55N10 | Singular homology and cohomology theory |
| 57K45 | Higher-dimensional knots and links |
References:
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