Does a wormhole survive a cosmological bounce?

We investigate whether a dynamical wormhole could survive in a universe that undergoes a cosmological bounce. First, the conditions under which a wormhole could persist from a contracting to an expanding phase of the cosmos are presented. Then, the only two known cosmological solutions of Einstein's equations representing wormholes are analyzed, and it is shown that both dynamical wormholes exist for all cosmic times on both sides of a bouncing universe and at the bounce itself. We also provide a detailed analysis of the causal structure of such spacetimes and the matter content of the wormhole. Finally, some possible astrophysical manifestations of surviving wormholes in a bouncing universe are mentioned. Our results show that, at least for the Kim and P\'erez-Raia Neto solutions, there is no topology change in the chosen cosmological model with a bounce.