Help Privacy Policy Disclaimer
  Advanced SearchBrowse




Journal Article

Signatures of topological branched covers


Kjuchukova,  Alexandra
Max Planck Institute for Mathematics, Max Planck Society;

External Resource
Fulltext (restricted access)
There are currently no full texts shared for your IP range.
Fulltext (public)

(Preprint), 380KB

Supplementary Material (public)
There is no public supplementary material available

Geske, C., Kjuchukova, A., & Shaneson, J. L. (2021). Signatures of topological branched covers. International Mathematics Research Notices, 2021(6), 4605-4624. doi:10.1093/imrn/rnaa184.

Cite as: https://hdl.handle.net/21.11116/0000-0007-745C-0
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 {\it topological} four-manifold and $B$ is locally flat, away from the
possible singularity. Owing to the presence of non-locally-flat points on $B$,
$X$ 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