We analyze a set of volume limited samples from the SDSS to study the dependence of galaxy colour on different environments of the cosmic web. We measure the local dimension of galaxies to determine the geometry of their embedding environments and find that filaments host a higher fraction of red galaxies than sheets at each luminosity. We repeat the analysis at a fixed density and recover the same trend which shows that galaxy colours depend on geometry of environments besides local density. At a fixed luminosity, the fraction of red galaxies in filaments and sheets increases with the extent of these environments. This suggests that the bigger structures have a larger baryon reservoir favouring higher accretion and larger stellar mass. We find that the mean colour of the red and blue populations are systematically higher in the environments with smaller local dimension and increases monotonically in all the environments with luminosity. We observe that the bimodal nature of the galaxy colour distribution persists in all environments and all luminosities, which suggests that the transformation from blue to red galaxy can occur in all environments.
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