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Polarization-insensitive multiple transparency windows are obtained with a graphene-based complementary meta-material structure in terahertz regions,which is composed of two kinds of monolayer graphene perforated in shapes of a cross and four identical split rings that construct a resonator.The geometric parameters of resonators are different from each other.Numerical and theoretical results show that the quantum effect of Autler-Townes splitting is the key factor for appearance of transparency windows within the resonant dips.Further investigation demonstrates that by employing the fourfold-symmetry graphene complementary structure,polarization-independent transparency windows can be achieved.Moreover,multiple transparency windows can be separately manipulated over a broad frequency range via adjusting the chemical potential of the corresponding graphene resonators,and the bandwidth as well as resonance strength can also be tuned by changing the relative displacement between resonators each consisting of a cross and four split rings.The proposed metamaterial structure may be utilized in some practical applications with requirements of no polarization-varied loss and slowing the light speed.