Given a smooth, compact four-manifold $ X $ viewed as a cobordism from the empty set to
its connected boundary, we demonstrate how to use the data of a trisection map $\pi …

Given a smooth, compact four-manifold X, we demonstrate how to use the data of a trisection
map π: X 4→ R 2 to compute the induced cobordism maps on Heegaard Floer homology. A …

Any smooth, closed oriented 4-manifold has a surface diagram of arbitrarily high genus g> 2
that specifies it up to diffeomorphism. The goal of this paper is to prove the following …

A Morse 2-function is a generic map from a manifold M of arbitrary finite dimension to a
surface B. Its critical set is a smooth 1-submanifold of M that maps to a cusped, immersed …

Broken Lefschetz fibrations are fibration structures analogous to Lefschetz fibrations in the
context of near-symplectic 4-manifolds. In the first part of this thesis, we discuss the …