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Determination and interpretation of Wigner-like photoionisation delays is one of the most active fields of attosecond science. Previous results have suggested that large photoionisation delays are associated with structured continua, but a quantitative relation between photoionisation cross sections and time delays has been missing. Here, we derive a Kramers–Kronig-like relation between these quantities and demonstrate its validity for (anti)resonances. This new concept defines a topological analysis, which rationalises the sign of photoionisation delays and thereby sheds new light on a long-standing controversy regarding the sign of the photoionisation delay near the Ar 3 s Cooper minimum. Our work bridges traditional photoionisation spectroscopy with attosecond chronoscopy and offers new methods for analysing and interpreting photoionisation delays.