# Ingrid's maths page

Some (at this point mostly unpublished) documents that came out of my PhD project. In this project, Morse theoretical type arguments were used study a curve complex obtained by generalising Harvey's curve complex to a fixed homology class. This complex, the homology curve complex, is closely related to a complex used for proving theorems about the Torelli group. Probably about the most surprising property of this complex is that there exist simple algorithms for calculating distances etc. Homology curve complex can also be used for studying surfaces in SxR and calculating commutator lengths.

Geometry of the Homology Curve Complex

Surfaces in SxR and paths in the homology curve complex

My thesis "The curve graph and surface construction in SxR" is here

My honours thesis is available here. This is about difficulties inherent in defining and working with singularities in spacetime.