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Search: MSC category 57Q45 ( Knots and links (in high dimensions) {For the low-dimensional case, see 57M25} )

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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 2002 (vol 45 pp. 131)

Przytycki, Józef H.; Rosicki, Witold
The Topological Interpretation of the Core Group of a Surface in $S^4$
We give a topological interpretation of the core group invariant of a surface embedded in $S^4$ \cite{F-R}, \cite{Ro}. We show that the group is isomorphic to the free product of the fundamental group of the double branch cover of $S^4$ with the surface as a branched set, and the infinite cyclic group. We present a generalization for unoriented surfaces, for other cyclic branched covers, and other codimension two embeddings of manifolds in spheres.

Categories:57Q45, 57M12, 57M05

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