The mosquito Aedes aegypti transmits some of the most important human arboviruses, including dengue, yellow fever and chikungunya viruses. It has a large genome containing many repetitive sequences, which has resulted in the genome being poorly assembled - there are 4,758 scaffolds, few of which have been assigned to a chromosome. To allow the mapping of genes affecting disease transmission, we have improved the genome assembly by scoring a large number of SNPs in recombinant progeny from a cross between two strains of Ae. aegypti, and used these to generate a genetic map. This revealed a high rate of misassemblies in the current genome, where, for example, sequences from different chromosomes were found on the same scaffold. Once these were corrected, we were able to assign 60% of the genome sequence to chromosomes and approximately order the scaffolds along the chromosome. We found that there are very large regions of suppressed recombination around the centromeres, which can extend to as much as 47% of the chromosome. To illustrate the utility of this new genome assembly, we mapped a gene that makes Ae. aegypti resistant to the human parasite Brugia malayi, and generated a list of candidate genes that could be affecting the trait.