clairobscure: Well the connection is still slightly controversial.
The standard argument is that Manichaeism ( founded by Mani around 250 CE as an apparent synthesis of Christian, Zoroastrian, and Buddhist thought ) spread throughout the Near East in a limited way, despite persecution by both the Romans and the Sassanians ( Mani was martyred in 276 ). Among its adherents was St. Augustine, who was a Manichaen for nine years in the 4th century and who’s writings were the main source on heresies in 11th century Europe ( more on that in a sec ). About the time Manichaeism per se started to fade in the 6th century, a heretical Christian sect known as the Paulicans ( they held the Apostle Paul in particularly high regard ) emerged in Armenia that apparently incorporated some elements of Manichaen philosophy within a more ostensibly Christian framework. This group reached the peak of their influence in the 9th century, but was persecuted by the Byzantines among others and a sizeable number were deported to the Balkans ( Thrace ). It was these deportees that transmitted elements of the heresy to the tenth century Bulgars were under the harsh conditions of the time it flourished and morphed into ( or merged with an earlier movement ) Bogomilism, which caught on - Spreading not only back into the Byzantine state, but also westwards where it merged with local groups to become the Catharism of the twelth and thirteenth century ( this last connection seems certain, though the exact sequence of when the missionaries began their work in the west is obscure - Catharism in the records emerges fairly full-blown in the mid-12th century ).
I don’t really have a single good, all-encompassing link for this, I’m afraid, but googling will give snippets, like this excerpt:
*As Prof. Dr. Edwin Yamauchi has pointed out in his important article Manichaeans: “The Paulician movement, which spread in Armenia from the seventh to the twelfth century --though it repudiated Manichaeism – resembled it in its dualistic views. The Paulicians came to Bulgaria in the tenth century and helped to develop the Bogomils, who flourished in the Balkans in the eleventh and twelfth centuries. The latter in turn stimulated the important Manichaean-like heresy of the Cathars or Albigensians in the twelfth and thirteenth centuries.”
In 1012, neo-Manichaeans appeared even in Germany. A group in Treves rejected infant baptism. These were the so- called Cathari – called ‘Bogomils’ in the East, and ‘Albigensians’ in the West. Instead of Biblical baptism, they substituted their own rite (called the consolamentum) – which also women were allowed to administer. Thereby, they laid on hands – and imposed John’s Gospel onto the candidate’s breast.
As Prof. Dr. Paul D. Steeves has indicated in his article The Paulicians and the Bogomils, "the Paulicians…held that only the Gospel and letters of Paul were divinely inspired. An evil deity…had inspired the rest of the New Testament, and the Old Testament. The Paulicians claimed that this evil deity was the creator and god of this world. The true God of heaven, they said, was opposed to all material things… Physical and material…sacraments…must have come from the same evil spirit…
"Some of the Bulgars adopted Paulician ideas into a new religious system that acquired the name ‘Bogomilism’… *
from here: http://www.reformed.org/sacramentology/lee/anab_002.html
However there are dissenting views that hold that the Bogomil/Cathar heresy was homegrown in Europe and that the only reason it has been identified with Manichaen tradition ( other than some superficial similarities ) was that a.) the only real writings that survive on them were written by their enemies and b.) authorities of the day leaned heavily on St. Augustine’s work to identify and categorize heresies - therefore they referred to the Cathars as ‘Manichees’ without really understanding the difference. This is the tack taken by Malcolm Lambert in his book The Cathars ( 1998, Blackwell Publishing Ltd. ) - A decent read by the way, if you’re interested in this sort of thing.
Here’s a brief web article on the Cathars that takes note of this scholarly dispute and mentions some other adherents of this minority view:
http://www.wisdomworld.org/additional/ListOfCollatedArticles/TheCathariOrAlbigenses.html
Myself, I like the standard view, but I am so far from an expert on the topic that MHO is hardly worth considering :).