Based on the timeline you've provided, the events and developments that can be directly tied to the invention of the cotton gin are:
B. industrialization in New England - The increase in cotton production due to the cotton gin fueled the growth of textile mills in New England, leading to industrialization in that region.
D. the spread of slavery - The cotton gin made cotton production more profitable, which in turn led to an increase in the demand for slave labor on plantations, contributing to the expansion of slavery in the South.
So, the two options that can be directly tied to the invention of the cotton gin are B and D.