Try reading the following:
Council of Chalcedon
The Fourth Ecumenical Council, held in 451, from 8 October until 1 November inclusive, at Chalcedon, a city of Bithynia in Asia Minor. Its principal purpose was to assert the orthodox Catholic doctrine against the heresy of Eutyches and the Monophysites, although ecclesiastical discipline and jurisdiction also occupied the council's attention.
Scarcely had the heresy of Nestorius concerning the two persons in Christ been condemned by the Council of Ephesus, in 431, when the opposite error of the Nestorian heresy arose. Since Nestorius so fully divided the Divine and the human in Christ that he taught a double personality or a twofold being in Christ, it became incumbent on his opponents to emphasize the unity in Christ and to exhibit the God-man, not as two beings but as one. Some of these opponents in their efforts to maintain a physical unity in Christ held that the two natures in Christ, the Divine and the human, were so intimately united that they became physically one, inasmuch as the human nature was completely absorbed by the Divine. Thus resulted one Christ not only with one personality but also with one nature. After the Incarnation, they said, no distinction could be made in Christ between the Divine and the human. The principal representatives of this teaching were Dioscurus, Patriarch of Alexandria, and Eutyches, an archimandrite or president of a monastery outside Constantinople. The Monophysitic error, as the new error was called (Gr. mone physis, one nature), claimed the authority of St. Cyril, but only through a misinterpretation of some expressions of the great Alexandrine teacher.
More
.
Wrong Council.
I think you mean this one.
CATHOLIC ENCYCLOPEDIA: Second Council of Constantinople
"In the meantime Vigilius had sent to the emperor (14 May) a document known as the first "Constitutum" (
Mansi, IX, 61-106), signed by himself and sixteen, mostly Western,
bishops, in which sixteen
heretical propositions of
Theodore of Mopsuestia were condemned, and, in five
anathematisms, his
Christological teachings repudiated; it was forbidden, however, to condemn his
person, or to proceed further in condemnation of the writings or the
person of Theodoret, or of the letter of Ibas."
"Vigilius, together with other opponents of the imperial will, as registered by the subservient court-prelates, seems to have been banished (
Hefele, II, 905), together with the faithful
bishops and
ecclesiastics of his suite, either to Upper
Egypt or to an island in the Propontis. Already in the seventh session of the council Justinian caused the name of Vigilius to be stricken from the
diptychs, without prejudice, however, it was said, to communion with the
Apostolic See. Soon the Roman
clergy and people, now freed by Narses from the Gothic yoke, requested the emperor to permit the return of the
pope, which Justinian agreed to on condition that Vigilius would recognize the late council. This Vigilius finally agreed to do, and in two documents (a letter to
Eutychius of Constantinople, 8 Dec., 553, and a second "Constitutum" of 23 Feb., 554, probably addressed to the Western episcopate) condemned, at last, the
Three Chapters (
Mansi, IX, 424-20, 457-88; cf. Hefele, II, 905-11)..."
New Advent tries to correct this discrepancy by stating:
"His opposition had never been based on
doctrinal grounds but on the decency and opportuneness of the measures proposed, the wrongful imperial
violence, and a delicate fear of injury to the authority of the
Council of Chalcedon, especially in the West."
However, the Constitum states that Theodoret and Ibas were orthodox (
A history of the councils of the church : from the original documents), and says this:
"We ordain and decree that it be permitted to no one belonging to any ecclesiastical order or office to write or bring forward or compose or teach anything contrary to the contents of this Constitutum in regard to the Three Chapters, or after this present definition to move any further question. And if anything has been done, said, or written by anyone anywhere about the Three Chapters contrary to what we here assert and decree...this in all ways we refute by the authority of the Apostolic See in which by the grace of God we preside."
Moreover, even if this was correct, New Advent doesn't seem to answer the question of how an Ecumenical Council can judge a Pope.