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Branched covers bounding rational homology balls

Paolo Aceto, Jeffrey Meier, Allison N Miller, Maggie Miller, JungHwan Park and András I Stipsicz

Algebraic & Geometric Topology 21 (2021) 3569–3599

Prime power–fold cyclic branched covers along smoothly slice knots all bound rational homology balls. This phenomenon, however, does not characterize slice knots. We give a new construction of nonslice knots that have the above property. The sliceness obstruction comes from computing twisted Alexander polynomials, and we introduce new techniques to simplify their calculation.

knot concordance group, branched covers
Mathematical Subject Classification
Primary: 57K10, 57M12
Received: 30 April 2020
Revised: 4 August 2020
Accepted: 19 November 2020
Published: 28 December 2021
Paolo Aceto
Laboratoire Paul Painlevé
Université de Lille
Jeffrey Meier
Department of Mathematics
Western Washington University
Bellingham, WA
United States
Allison N Miller
Department of Mathematics and Statistics
Swarthmore College
Swarthmore, PA
United States
Maggie Miller
Department of Mathematics
Princeton University
Princeton, NJ
United States
Department of Mathematics
Massachusetts Institute of Technology
Cambridge, MA
United States
JungHwan Park
Department of Mathematical Sciences
Korea Advanced Institute of Science and Technology
South Korea
András I Stipsicz
Rényi Institute of Mathematics