What is the role of women in the big sleep?

Women in the big sleep are there to give the novel some mystery. Carmen and Vivien are mysterious characters who, on the whole, are quite unpredictable. Carmen, who is somewhat deranged, is more crazy than mysterious but the way that she and Marlowe interact gives her a sense of mystery. Vivien has known about the murder of her husband, Rusty Regan, all along and spends her time trying to be misleading.
Women are their for mystery.