Handle decompositions of rational homology balls and Casson-Gordon invariants

Paolo Aceto (1) , Marco Golla (2, 3) , Ana G Lecuona (4)

1 MPIM - Max Planck Institute for Mathematics
2 Mathematical Institute, University of Oxford
3 LMJL - Laboratoire de Mathématiques Jean Leray
4 I2M - Institut de Mathématiques de Marseille

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.

Mots clés: SINGULARITIES; SURGERIES; SURFACES; CURVES; LINKS; KNOTS

Domaines: Topologie géométrique [math.GT]

Paolo Aceto, Marco Golla, Ana G Lecuona. Handle decompositions of rational homology balls and Casson-Gordon invariants. Proceedings of the American Mathematical Society, 2018, 146 (9), pp.4059-4072. ⟨10.1090/proc/14035⟩. ⟨hal-01485351⟩