  Euclidean d=3 SU(2) Yang-Mills-Chern-Simons (YMCS) theory, including
Georgi-Glashow (GGCS) theory, may have solitons in the presence of appropriate
mass terms. For integral CS level k and for solitons carrying integral CS
number, YMCS is gauge-invariant and consistent. However, individual solitons
such as sphalerons and linked center vortices with CS number of 1/2 and
writhing center vortices with arbitrary CS number are non-compact; a condensate
of them threatens compactness of the theory. We study various forms of the
non-compact theory in the dilute-gas approximation, treating the parameters of
non-compact large gauge transformations as collective coordinates. We conclude:
1) YMCS theory dynamically compactifies; non-compact YMCS have infinitely
higher vacuum energy than compact YMCS. 2) An odd number of sphalerons is
associated with a domain- wall sphaleron, a pure-gauge configuration on a
closed surface enclosing them and with a half-integral CS number. 3) We
interpret the domain-wall sphaleron in terms of fictitious closed Abelian
magnetic field lines that express the links of the Hopf fibration. Sphalerons
are over- and under-crossings of knots in the field lines; the domain-wall
sphaleron is a superconducting wall confining these knots to a compact domain.
4) Analogous results hold for center vortices and nexuses. 5) For a CS term
induced with an odd number of fermion doublets, domain-wall sphalerons are
related to non-normalizable fermion modes. 6) GGCS with monopoles is
compactified with center-vortex-like strings.
