U(g) 
knots 
U(g)^{m} 
links 
the product m of U(g) 
connected sums:

the coproduct Δ of U(g) 
doubling: 
the bracket [ , ] of g 
the GoussarovHabiro theory of claspers 
the PoincaréBirkhoffWitt theorem 
formal PBW, eigenspaces of cabling 
the HarishChandraDuflo isomorphism 
Wheeling, 1+1=2:

ChernSimons theory 
configuration space integrals 
integration on g 
formal Gaussian integration, 3manifolds 
Lie bialgebras 
directed diagrams, virtual knots 
associators and the pentagon, 6jsymbols 
paranthesized tangles, knotted trivalent graphs 