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Search: MSC category 57Q10 ( Simple homotopy type, Whitehead torsion, Reidemeister-Franz torsion, etc. [See also 19B28] )

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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 mapCategories:57N65, 57R67, 57Q10

2. CMB 2008 (vol 51 pp. 535)

Csorba, Péter
 On the Simple $\Z_2$-homotopy Types of Graph Complexes and Their Simple $\Z_2$-universality We prove that the neighborhood complex $\N(G)$, the box complex $\B(G)$, the homomorphism complex $\Hom(K_2,G)$and the Lov\'{a}sz complex $\L(G)$ have the same simple $\Z_2$-homotopy type in the sense of Whitehead. We show that these graph complexes are simple $\Z_2$-universal. Keywords:graph complexes, simple $\Z_2$-homotopy, universalityCategories:57Q10, 05C10, 55P10

3. CMB 2006 (vol 49 pp. 55)

Dubois, Jérôme
 Non Abelian Twisted Reidemeister Torsion for Fibered Knots In this article, we give an explicit formula to compute the non abelian twisted sign-deter\-mined Reidemeister torsion of the exterior of a fibered knot in terms of its monodromy. As an application, we give explicit formulae for the non abelian Reidemeister torsion of torus knots and of the figure eight knot. Keywords:Reidemeister torsion, Fibered knots, Knot groups, Representation space, $\SU$, $\SL$, Adjoint representation, MonodromyCategories:57Q10, 57M27, 57M25