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We give an explicit algorithm for computing the linking number between <jats:italic>K<\/jats:italic> and <jats:italic>L<\/jats:italic> in terms of a presentation of\u00a0<jats:italic>M<\/jats:italic> as an irregular dihedral three-fold cover of\u00a0<jats:inline-formula><jats:alternatives><jats:tex-math>$$S^3$$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                  <mml:msup>\n                    <mml:mi>S<\/mml:mi>\n                    <mml:mn>3<\/mml:mn>\n                  <\/mml:msup>\n                <\/mml:math><\/jats:alternatives><\/jats:inline-formula> branched along a knot <jats:inline-formula><jats:alternatives><jats:tex-math>$$\\alpha \\subset S^3$$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                  <mml:mrow>\n                    <mml:mi>\u03b1<\/mml:mi>\n                    <mml:mo>\u2282<\/mml:mo>\n                    <mml:msup>\n                      <mml:mi>S<\/mml:mi>\n                      <mml:mn>3<\/mml:mn>\n                    <\/mml:msup>\n                  <\/mml:mrow>\n                <\/mml:math><\/jats:alternatives><\/jats:inline-formula>. Since every closed, oriented three-manifold admits such a presentation, our results apply to all (well-defined) linking numbers in all three-manifolds. Furthermore, ribbon obstructions for a knot\u00a0<jats:inline-formula><jats:alternatives><jats:tex-math>$$\\alpha $$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                  <mml:mi>\u03b1<\/mml:mi>\n                <\/mml:math><\/jats:alternatives><\/jats:inline-formula> can be derived from dihedral covers of\u00a0<jats:inline-formula><jats:alternatives><jats:tex-math>$$\\alpha $$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                  <mml:mi>\u03b1<\/mml:mi>\n                <\/mml:math><\/jats:alternatives><\/jats:inline-formula>. The linking numbers we compute are necessary for evaluating one such obstruction. This work is a step toward testing potential counter-examples to the Slice-Ribbon Conjecture, among other applications.<\/jats:p>","DOI":"10.1007\/s00454-021-00287-3","type":"journal-article","created":{"date-parts":[[2021,7,6]],"date-time":"2021-07-06T15:04:29Z","timestamp":1625583869000},"page":"435-463","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Linking Numbers in Three-Manifolds"],"prefix":"10.1007","volume":"66","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-2834-0897","authenticated-orcid":false,"given":"Patricia","family":"Cahn","sequence":"first","affiliation":[]},{"given":"Alexandra","family":"Kjuchukova","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2021,7,6]]},"reference":[{"issue":"1","key":"287_CR1","doi-asserted-by":"publisher","first-page":"263","DOI":"10.1007\/BF02940679","volume":"10","author":"C Bankwitz","year":"1934","unstructured":"Bankwitz, C., Schumann, H.G.: \u00dcber viergeflechte. 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