University of Pennsylvania ScholarlyCommons Publicly Accessible Penn Dissertations 2015 On the Classification of Irregular Dihedral Branched Covers of Four-Manifolds Alexandra Kjuchukova University of Pennsylvania,
[email protected] Follow this and additional works at: https://repository.upenn.edu/edissertations Part of the Mathematics Commons Recommended Citation Kjuchukova, Alexandra, "On the Classification of Irregular Dihedral Branched Covers of Four-Manifolds" (2015). Publicly Accessible Penn Dissertations. 1817. https://repository.upenn.edu/edissertations/1817 This paper is posted at ScholarlyCommons. https://repository.upenn.edu/edissertations/1817 For more information, please contact
[email protected]. On the Classification of Irregular Dihedral Branched Covers of Four-Manifolds Abstract We prove a necessary condition for a four-manifold $Y$ to be homeomorphic to a $p$-fold irregular dihedral branched cover of a given four-manifold $X$, with a fixed branching set $B$. The branching sets considered are closed oriented surfaces embedded locally flatly in $X$ except at one point with a specified cone singularity. The necessary condition obtained is on the rank and signature of the intersection form of $Y$ and is given in terms of the rank and signature of the intersection form of $X$, the self-intersection number of $B$ in $X$ and classical-type invariants of the singularity. Secondly, we show that, for an infinite class of singularities, the necessary condition is sharp. That is, if the singularity is a two-bridge slice knot, every pair of values of the rank and signature of the intersection form which the necessary condition allows is in fact realized by a manifold dihedral cover.