= Heegaard Floer homology
{c}
{title2=$HF^\circ(Y,\mathfrak s)$}
Heegaard Floer homology assigns groups $HF^\circ(Y,\mathfrak s)$ to a closed oriented three-manifold with a <Spin-c structure>. A pointed <Heegaard diagram> of genus $g$ gives product <Lagrangian tori> $\mathbb T_\alpha,\mathbb T_\beta\subset\operatorname{Sym}^g(\Sigma)$; the <chain complex> is generated by their intersection points and its differential counts <Whitney disk classes> represented by holomorphic disks. The minus, infinity, plus and hat versions use different powers or quotients of the variable $U$. The <Heegaard Floer cobordism maps> and the <Mixed Heegaard Floer invariant> relate these groups to smooth four-dimensional topology.
Back to article page
