A River.
Agastya created a child from the most beautiful parts of creation. It was born as Lopamudra to King Kavera and Agastya married Lopamudra. When Agastya had to travel for a long time, he turned Lopamudra into water and left her in his water vessel. When it was taking too long for her, she flowed out as Kaveri, Kavera’s daughter.
First myth: Kaveri asked Vishnu to be more holy than Ganga. Vishnu could not fulfill this wish because Ganga had come into contact with his feet. He offered Kaveri to be allowed to become his garland, thus very close to his heart. Three Vishnu temples are located on an island surrounded by the kaveri.
Second myth: Ganga, Kaveri, Yamuna and Sarasvati once played together. A Gandharva saw them and adored them. Each of the four now claimed that he had adored her alone. There was a dispute. Yamuna and Sarasvati calmed down at some point, Ganga and Kaveri went to Vishnu.
Ganga explained to Vishnu that since she once came in contact with his feet, she was more sublime than Kaveri. Vishnu agreed with her. Kaveri was disappointed. She meditated on Vishnu and he promised her to rest here on its banks.
In Srirangam she is Vishnu’s resting place. In Tirucherai she is His mother. In Tiruindhalur he takes them on his head and equates her with Ganga, who flowed through Shiva’s hair. The places are Divya Desham.