Colosians 1:23 wrote:τοῦ εὐαγγελίου οὗ ἠκούσατε, τοῦ κηρυχθέντος ἐν πάσῃ κτίσει τῇ ὑπὸ τὸν οὐρανόν, οὗ ἐγενόμην ἐγὼ Παῦλος διάκονος.
The entire phrase
The phrase is in the genitive not because it is absolute
("free standing" - not reliant on in relation to anything else), but because it is related to ἡ ἐλπίς "the hope". The entire phrase" that Carl alerted you to above is
in the genitive, and if it were not in the genitive it would be
Part of Colosians 1:23 changed to the accusative wrote:τὸ εὐαγγέλιον ὃ ἠκούσατε, τὸ κηρυχθὲν ἐν πάσῃ κτίσει τῇ ὑπὸ τὸν οὐρανόν, οὗ ἐγενόμην ἐγὼ Παῦλος διάκονος.
We can see in this composition that to change the whole phrase to accusative, we only have to change it at two points - the noun τοῦ εὐαγγελίου which goes to τὸ εὐαγγέλιον, and the participle τοῦ κηρυχθέντος which changes to τὸ κηρυχθὲν. This is a general rule; the participle generally agrees with the noun it is saying something about
. The article before the participle is a "article" in the true sense of the word (Greek ἄρθρον
"joint (like between bones)") putting the noun and participle together.
The other two genitives remain as they are in the phrase. Why? Because they are in the genitive for other reasons. What are they?
It is not so easy to explain why the οὗ of οὗ ἠκούσατε is in the genitive, but it is. I would expect to see it in the accusative because ἀκούειν takes an accusative of what is heard (and a genitive of the person who is heard), so evidently that might not be the explanation here. It is probably false attraction into the genitive (i.e. everything else is in the genitive so it is "accidently" put into the genitive too).
In the final phrase οὗ ἐγενόμην ἐγὼ Παῦλος διάκονος, οὗ is in the genitive because it goes with διάκονος "minsiter". To express that another way we could write Ἐγὼ Παῦλος ἐγενόμην διάκονος τοῦ εὐαγγελίου ὃ ἠκούσατε, τοῦ κηρυχθέντος ἐν πάσῃ κτίσει τῇ ὑπὸ τὸν οὐρανόν - I don't know this as a rule, but from reading exprience I would say that having the second relative in the genitive would do more to attract the ὃ ἠκούσατε to οὗ ἠκούσατε than just the genitive after a noun.
For this to be a genitive absolute, it would probably be at the start of a phrase (or paragraph), with other stuff out in front such as
SGH's use of Psalm 99:1, 2 (LXX) with a genitive absolute adapted from Colosians 1:23 in front wrote:τοῦ εὐαγγελίου κηρυχθέντος ἐν πάσῃ κτίσει τῇ ὑπὸ τὸν οὐρανόν, ἀλαλάζουσιν τῷ Κυρίῳ πᾶσα ἡ γῆ καὶ εἰσέρχονται ἐνώπιον αὐτοῦ ἐν ἀγαλλιάσει. ἐν ταῖς αὐλαῖς αὐτοῦ ἐν ὕμνοις ἐξομολογοῦνται αὐτῷ καὶ παρὰ τὰς πύλας αὐτοῦ αἰνοῦσιν τὸ ὄνομα αὐτοῦ