= Monopole core and mass scales in an SU(5) transition
{title2=$M_M\sim4\pi\eta/g$}
For <simply connected space> $SU(5)$ broken to the connected <Standard Model> subgroup, the exact homotopy sequence gives $\pi_2(G/H)\cong\pi_1(H)\cong\mathbb Z$. Stable <magnetic monopoles> form. Their gauge and scalar cores have scales $(g\eta)^{-1}$ and $(\sqrt\lambda\eta)^{-1}$; their masses are $M_M\sim4\pi\eta/g$ times a dimensionless profile factor. The physical subgroup is $(SU(3)\times SU(2)\times U(1))/\mathbb Z_6$, which retains an infinite-cyclic fundamental group.
// Target: cosmology.bigb
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