Carbomer
In plain terms
The gel-maker. A large synthetic molecule that thickens watery products into smooth gels and creams. It sits on the surface of the skin rather than sinking in, and it is about as low-risk as thickeners get, with one manufacturing footnote.
What the evidence shows
Carbomer is a high-molecular-weight polymer of acrylic acid used to thicken and stabilize gels, creams, and lotions. Because the molecule is so large it stays on the surface of the skin instead of being absorbed, and the CIR panel rates it nontoxic with little or no irritation at the levels used in products; allergy to it is rare. The one footnote is how it is made. Some older carbomers were polymerized in benzene, a known carcinogen, and could hold a residual trace of it, and the CIR safety conclusion is conditional on the polymer not being made in benzene. Modern production has largely moved to benzene-free solvents like ethyl acetate, and the EU caps benzene in cosmetic ingredients below 0.1%, so the typical carbomer on the market today is benzene-free. This is the same kind of resolved-manufacturing point as refined petrolatum: the concern is real in principle but handled by current standards, while the polymer itself is inert and does not penetrate. Carbomer also serves in eye gels and artificial tears, where trials find it well tolerated even on the sensitive eye surface. For most products it is a benign structural ingredient.
On the label
Listed as carbomer, sometimes with a number like 940, or as Carbopol. Nothing to avoid for most people, and reputable EU-market products use benzene-free grades. If you do react to a gel, it is more often the active ingredients or preservatives than the carbomer itself.