||Histone demethylase required for G2/M phase cell cycle progression. Specifically demethylates dimethylated 'Lys-36' (H3K36me2) of histone H3, an epigenetic repressive mark, thereby acting as a transcription activator. Regulates expression of CCNA1 (cyclin-A1), leading to regulate cancer cell proliferation. In a complex with coregulator RCCD1, is also able to demethylate trimethylated 'Lys-36' (H3K36me3) of histone H3. Plays a role in transcriptional repression of satellite repeats, possibly by regulating H3K36 methylation levels in centromeric regions together with RCCD1. Possibly together with RCCD1, involved in proper mitotic spindle organization and chromosome segregation. Plays a role in regulating alpha-tubulin acetylation and cytoskeletal microtubule stability (By similarity). Might function as a protein hydroxylase (Potential). Under stress conditions that cause a DNA damage response, acts as a histone protease by cleaving the N-terminal tail of histone H3 at the carboxyl side of monomethyl-lysine (Kme1) residues, preferably at monomethylated 'Lys-9' (H3K9me1). The histone variant H3F3A is the major target for cleavage.