Abstract: A systematic comparison of the negative parity yrast states' energy level structures indicates a level inversion between the9/2^- and the 11/2^- in ⁵⁵Co, and suggests that ⁵³Co and ⁵⁷Co might exhibit strong collective effects. Shell model calculations based on the GXPF1A effective interaction accurately reproduce yrast state halo state energy levels of these nuclei, as well as the corresponding experimental magnetic moments and electric quadrupole moments. The shell model results show that the dominant component of proton configuration for the ground state 7/2^- in ⁵³⁻⁶⁵Co is \pi\left(1f_7/2\right)^7. The excited states 9/2^- and 11/2^- in ⁵⁵Co involve a competition between 1f_7/2 proton excitation and 1f_7/2 neutron excitation, leading to a possible level inversion between the these states. Moreover, by using the Constrained Hartree-Fock (CHF) method to study the quadrupole deformation characteristics of ⁵³Co^{, 55}Co and ⁵⁷Co, and combining the average occupancy numbers and configurations obtained from shell model calculations, the reasons for higher the excited state energies of ⁵⁵Co compared to other Co isotopes were analyzed.