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Search: MSC category 57R65 ( Surgery and handlebodies )

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1. CMB 2007 (vol 50 pp. 481)

Blanlœil, Vincent; Saeki, Osamu
Concordance des nœuds de dimension $4$
We prove that for a simply connected closed $4$-dimensional manifold, its embeddings into the sphere of dimension $6$ are all concordant to each other.

Keywords:concordance, cobordisme, n{\oe}ud de dimension $4$, chirurgie plongée
Categories:57Q45, 57Q60, 57R40, 57R65, 57N13

2. CMB 1999 (vol 42 pp. 149)

Boyer, S.; Zhang, X.
A Note on Finite Dehn Fillings
Let $M$ be a compact, connected, orientable 3-manifold whose boundary is a torus and whose interior admits a complete hyperbolic metric of finite volume. In this paper we show that if the minimal Culler-Shalen norm of a non-zero class in $H_1(\partial M)$ is larger than $8$, then the finite surgery conjecture holds for $M$. This means that there are at most $5$ Dehn fillings of $M$ which can yield manifolds having cyclic or finite fundamental groups and the distance between any slopes yielding such manifolds is at most $3$.

Categories:57M25, 57R65

3. CMB 1998 (vol 41 pp. 374)

Young, Carmen M.
Normal invariants of lens spaces
We show that normal and stable normal invariants of polarized homotopy equivalences of lens spaces $M = L(2^m;\r)$ and $N = L(2^m;\s)$ are determined by certain $\ell$-polynomials evaluated on the elementary symmetric functions $\sigma_i(\rsquare)$ and $\sigma_i(\ssquare)$. Each polynomial $\ell_k$ appears as the homogeneous part of degree $k$ in the Hirzebruch multiplicative $L$-sequence. When $n = 8$, the elementary symmetric functions alone determine the relevant normal invariants.

Categories:57R65, 57S25

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