On certain fibred ribbon disc pairs

Aitchison, Iain R.; Silver, Daniel S.

doi:10.1090/S0002-9947-1988-0933305-5

On certain fibred ribbon disc pairs
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by Iain R. Aitchison and Daniel S. Silver PDF

Trans. Amer. Math. Soc. 306 (1988), 529-551 Request permission

Abstract:

We prove that for any free group automorphism ${\phi ^{\ast }}$ having a specified form there exists an invertible ribbon disc pair $({B^4}, {D^2})$ such that the closure of ${B_4} - \operatorname {nbd} ({D^2})$ fibres over the circle with fibre a handlebody and monodromy equal to ${\phi ^{\ast }}$. We apply this to obtain results about ribbon $1$- and $2$-knots.

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