In:
International Mathematics Research Notices, Oxford University Press (OUP), Vol. 2021, No. 6 ( 2021-03-12), p. 4605-4624
Abstract:
Let $X^4$ and $Y^4$ be smooth manifolds and $f: X\to Y$ a branched cover with branching set $B$. Classically, if $B$ is smoothly embedded in $Y$, the signature $\sigma (X)$ can be computed from data about $Y$, $B$ and the local degrees of $f$. When $f$ is an irregular dihedral cover and $B\subset Y$ smoothly embedded away from a cone singularity whose link is $K$, the second author gave a formula for the contribution $\Xi (K)$ to $\sigma (X)$ resulting from the non-smooth point. We extend the above results to the case where $Y$ is a topological four-manifold and $B$ is locally flat, away from the possible singularity. Owing to the presence of points on $B$ which are not locally flat, $X$ in this setting is a stratified pseudomanifold, and we use the intersection homology signature of $X$, $\sigma _{IH}(X)$. For any knot $K$ whose determinant is not $\pm 1$, a homotopy ribbon obstruction is derived from $\Xi (K)$, providing a new technique to potentially detect slice knots that are not ribbon.
Type of Medium:
Online Resource
ISSN:
1073-7928
,
1687-0247
DOI:
10.1093/imrn/rnaa184
Language:
English
Publisher:
Oxford University Press (OUP)
Publication Date:
2021
detail.hit.zdb_id:
1465368-0
SSG:
17,1
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