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 concordance, cobordisme, n{\oe}ud de dimension $4$, chirurgie plongée

MSC Classifications:

57Q45, 57Q60, 57R40, 57R65, 57N13 show english descriptions Knots and links (in high dimensions) {For the low-dimensional case, see 57M25}
Cobordism and concordance
Embeddings
Surgery and handlebodies
Topology of $E^4$, $4$-manifolds [See also 14Jxx, 32Jxx] 57Q45 - Knots and links (in high dimensions) {For the low-dimensional case, see 57M25}
57Q60 - Cobordism and concordance
57R40 - Embeddings
57R65 - Surgery and handlebodies
57N13 - Topology of $E^4$, $4$-manifolds [See also 14Jxx, 32Jxx]

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