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We investigate the non-Abelian Bianchi identities in pure SU(2) lattice Yang-Mills theory in three and four dimensions. The non-Abelian Stokes theorem proposed recently allows to formulate the Bianchi identities in terms of local physical fluxes. Then the violation of Bianchi identities becomes a well defined concept ultimately related to chromomagnetic fields degeneracy points. We present numerical evidences that in D=4 the suppression of the Bianchi identities violation destroys confinement while the removal of the degeneracy points drives the theory to the topologically non-trivial sector.

Bianchi Identities and Degeneracy of Chromomagnetic Fields in SU(2) Gluodynamics