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We have given a new description of the lattice Yang-Mills theory a laCho-Faddeev-Niemi-Shabanov, which has enabled us to confirm in agauge-independent manner "Abelian"-dominance and magnetic-monopole dominance inthe Wilson loop average, yielding a gauge-independent dual superconductorpicture for quark confinement. In particular, we have given a new procedure(called reduction) for obtaining a gauge-independent magnetic monopole from agiven Yang-Mills field. In this talk, we demonstrate how some of knowntopological configurations in the SU(2) Yang-Mills theory such as merons andinstantons generate closed loops of magnetic-monopole current as the quarkconfiner, both of which are characterized by the gauge-invariant topologicalindex, topological charge (density) and magnetic charge (density),respectively. We also try to detect which type of topological configurationsexist in the lattice data involving magnetic-monopole loops generated by MonteCarlo simulation. Here we apply a new geometrical algorithm based on"computational homology" to discriminating each closed loop from clusters ofmagnetic-monopole current, since the magnetic-monopole current on a lattice isinteger valued.

Topological configurations of Yang-Mills field responsible for magnetic-monopole loops as quark confiner