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63 pagesInternational audienceWe investigate the problem of characterising the family of strongly quasipositive links which have definite symmetrised Seifert forms and apply our results to the problem of determining when such a link can have an L-space cyclic branched cover. In particular, we show that if δn​=σ1​σ2​…σn−1​ is the dual Garside element and b=δnk​P∈Bn​ is a strongly quasipositive braid whose braid closure b is definite, then k≥2 implies that b is one of the torus links T(2,q),T(3,4),T(3,5) or pretzel links P(−2,2,m),P(−2,3,4). Applying Theorem 1.1 of our previous paper we deduce that if one of the standard cyclic branched covers of b is an L-space, then b is one of these links. We show by example that there are strongly quasipositive braids δn​P whose closures are definite but not one of these torus or pretzel links. We also determine the family of definite strongly quasipositive 3-braids and show that their closures coincide with the family of strongly quasipositive 3-braids with an L-space branched cover
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