Handle decompositions of rational balls and Casson-Gordon invariants
arXiv:1610.10032
Abstract
Given a rational homology sphere which bounds rational homology balls, we investigate the complexity of these balls as measured by the number of 1-handles in a handle decomposition. We use Casson-Gordon invariants to obtain lower bounds which also lead to lower bounds on the fusion number of ribbon knots. We use Levine-Tristram signatures to compute these bounds and produce explicit examples.
12 pages, 1 figure. Updated version following referee's advice. Accepted for publication in Proceedings of the American Mathematical Society