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Search: MSC category 57N65 ( Algebraic topology of manifolds )

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1. CMB 2008 (vol 51 pp. 508)

Cavicchioli, Alberto; Spaggiari, Fulvia
A Result in Surgery Theory
We study the topological $4$-dimensional surgery problem for a closed connected orientable topological $4$-manifold $X$ with vanishing second homotopy and $\pi_1(X)\cong A * F(r)$, where $A$ has one end and $F(r)$ is the free group of rank $r\ge 1$. Our result is related to a theorem of Krushkal and Lee, and depends on the validity of the Novikov conjecture for such fundamental groups.

Keywords:four-manifolds, homotopy type, obstruction theory, homology with local coefficients, surgery, normal invariant, assembly map
Categories:57N65, 57R67, 57Q10

2. CMB 1999 (vol 42 pp. 257)

Austin, David; Rolfsen, Dale
Homotopy of Knots and the Alexander Polynomial
Any knot in a 3-dimensional homology sphere is homotopic to a knot with trivial Alexander polynomial.

Categories:57N10, 57M05, 57M25, 57N65

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