Abel's work spans two broad fields of inquiry. The first is gender and sexuality, psychoanalysis and 20th-century fiction (with a focus on Virginia Woolf). Her first book, Virginia Woolf and the Fictions of Psychoanalysis (1989), uncovered the legacies of Freud and Melanie Klein in Woolf’s narrative strategies. Her forthcoming book Odd Affinities: Virginia Woolf’s Shadow Genealogies (2024), explores the afterlives of Virginia Woolf in unexpected places and cultural traditions across the twentieth century: not the popular cultural appropriations, but the subtle resonances and subtextual conversations that are audible in writers as diverse as Nella Larsen, James Baldwin, Roland Barthes, and W.G. Sebald.
Her second area of inquiry is race, cultural studies and visuality. This inquiry culminated in her second book, Signs of the Times: The Visual Politics of Jim Crow (2010), which charts the cultural history of segregation signs through their mediation by photography.