If the question is really about the river mentioned by a commentator, there is no river in Tamil Nadu called Kāyakuṭī. If one considers the possibility that this name is a translation of some Tamil name, one has to allow for ‘losses in translation’. According to Monier Williams, kāya also means "assemblage , collection , multitude SaddhP.” This seems to be a synonym of saṅgha (perhaps referring to the legendary Tamil assembly in Madurai) or a translation of ‘Ta. Kūṭal’, another name of the city of Madurai. 

If it was related to the city called uraga, there was a discussion in Indology earlier such as
http://list.indology.info/pipermail/indology_list.indology.info/1999-March/016494.html 

I was not able to navigate and get to all the posts from this link. You may want to do a search on ‘uraga’ and look at the posts.

Regards,
Palaniappan

On Aug 29, 2017, at 9:32 AM, Christophe Vielle via INDOLOGY <indology@list.indology.info> wrote:

The name of this river is reminding of 'Kāyal', the name of the emporium in the delta of the Tamraparni (Tinnevelly District) referred to by Marco Polo (https://ebooks.adelaide.edu.au/p/polo/marco/travels/book3.21.html - cf. Kólkhoi emporion, Ptolemy Geogr. 7, 1, 10). But the Tamil word kāyal ('backwater, mouth of a stream") is far from the meaning of "Curve of the body" (kuṭī is found in several words for/names of "curving" rivers). The Tāmraparṇī  herself is described by Kālidāsa in 4.50 (53  crit. ed. Goodall & Isaacson).
This explanation of Nāga(/Uraga)-pura as a city on the border of the Kāyakuṭī  river in the  Pāṇḍya country was already made by  Dakṣiṇāvartanātha  (13th-14th c.) in his unpublished dīpikā on the Raghuvaṃśa according to N. P. Unni (Highways and Byways in Sanskrit Literature, Delhi: New Bharatiya Book Corporation, 2012, p. 159, who relies on a KUML transcript-manuscript). It is in this case (like in other) the source of  Aruṇagirinātha (contemporary of  Mallinātha, early 15th century - the latter who also sometimes uses Dakṣiṇāvartanātha has possibly misread his source here or, as you guess, his text has been later corrupted), himself followed by  Nārāyaṇa Paṇḍita.
The commentary of Vallabhadeva could be useful here, but I have not Goodall & Isaacson edition at hand.
On his side, the commentator Hemādri says: uragākhyasyeti kalpitārtham.
Best wishes,
Christophe Vielle

Le 28 août 2017 à 21:34, Krishnaprasad G via INDOLOGY <indology@list.indology.info> a écrit :

Dear all

In Raghuvamsa 6th Canto and Verse 58 or 59 
अथोरगाख्यस्य पुरस्य नाथं first foot says about Nagapura or Uragapura 
Mallinatha explains as कान्यकुब्जतीरवर्तिनागपुरस्य but this seems to be a mistake as Kanouj is on the North of India , whereas the poet in further verses clearly places it on the south. 

And on further search I found Arunagirinatha and Narayana in the commentary to the above mentioned verse give the details as the place  in the bank of the river कायकुटी
पाण्ड्येषु कायकुटी नाम नदी प्रवहति तस्मिन् तीरे नागपुराख्यं...

Does any one knows about this river or its modern name kindly inform.

I also believe that even Mallinatha has written कायकुटी as the name is not famous that must be due to लिपिसारूप्य scribal error occurred
Thanks
Correction :
Not तस्मिन् 
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