Final answer:
The opponents of slavery who held their own election and wrote their own constitution in Kansas were known as Free Soilers, who rejected the pro-slavery Lecompton Constitution and created an anti-slavery legislature and constitution in Topeka.
Step-by-step explanation:
When the election was held in Kansas, slavery supporters flowed into the state and installed a pro-slavery legislature; opponents of slavery, known as Free Soilers, held their own elections and wrote their own constitutions.
The Free Soilers opposed the Lecompton Constitution, which was a pro-slavery document that had been created by the pro-slavery legislature. This document offered a choice between a constitution with slavery or a constitution with no slavery that still protected slave property, which the Free Soilers referred to as the "great swindle."
In response to fraudulent pro-slavery government actions and the undemocratic Lecompton Constitution, the Free Soilers convened in Topeka and established a constitution excluding slavery, creating a stark division and leading to the establishment of two competing legislatures and constitutions within Kansas.