We investigate braid invariants, such as the writhe and the fractional Dehn twist coefficient (FDTC), that arise as the homogenization of a concordance homomorphism, such as tau and Upsilon from the Heegaard Floer tool box. After providing a new characterization of the FDTC, we turn to connections with low-dimensional topology via the concept of homogenization of knot invariants. Concretely, we view the slice Bennequin inequality---a celebrated  inequality due to Kronheimer-Mrowka and Rudolph that relates a knot invariant (the smooth 4-genus) and a braid invariant (the writhe)---as a special case of relating knot concordance homomorphisms and their homogenizations. As an application we find that the slice-Bennequin inequality holds with the FDTC in place of the writhe. Teaser: As a motivation for the concept of homogenization, this talk features a neat construction of the field of real numbers you probably dont know about.