On the slice genus and some concordance invariants of links

Abstract

We introduce a new class of links for which we give a lower bound for the slice genus $g_{\ast }$, using the generalized Rasmussen invariant. We show that this bound, in some cases, allows one to compute $g_{\ast }$ exactly; in particular, we compute $g_{\ast }$ for torus links. We also study another link invariant: the strong slice genus $g_{\ast }^{\ast }$. Studying the behaviour of a specific type of cobordisms in Lee homology, a lower bound for $g_{\ast }^{\ast }$ is also given.

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