In the early 2000s, Ozsv\'{a}th and Szab\'{o} introduced a collection of invariants for 3--manifolds and 4--manifolds called Heegaard Floer homology. To a 3--ma

The authors construct Heegaard Floer theory for 3-manifolds with connected boundary. The theory associates to an oriented, parametrized two-manifold a different

The Heegaard Floer hat invariant is defined on closed 3-manifolds, with a related invariant for 4-dimensional cobordisms, forming a 3+1 topological quantum fiel

Mathematical gauge theory studies connections on principal bundles, or, more precisely, the solution spaces of certain partial differential equations for such c