Heegaard Floer Homology — Spin^c Structure Exercise

My notes on Spin^c structures on oriented closed 3-manifolds.

One of the main goals is to establish the fundamental correspondence: \[ \mathrm{Spin}^c(Y) \cong H^2(Y; \mathbb{Z}) \]

This work is based on an exercise from An Introduction to Heegaard Floer Homology by Peter Ozsváth and Zoltán Szabó (Exercise 6.3, p. 13).