| Abstract: |
Heegaard splittings, a key area of 3-manifold theory, deal with one of the difficulties in the study of 3-manifolds: visualization. This technique gives a convenient way to assimilate a 3-manifold for the human mind, by splitting it into smaller 'visible' pieces. Whilst the traditional field of two-sided Heegaard splittings decomposes a 3-manifold into two pieces, having split along an embedded two-sided surface, the one-sided analogue - a one-sided Heegaard splitting - splits the manifold instead along an embedded non-orientable surface, resulting in a single piece. I will describe this technique through concrete examples, making it accessible to those without a background in the field. In the context of two-sided splittings, there are obvious analogues to be pursued in the one-sided case. I will discuss some of these, illustrating both similarities and differences, as established in my thesis.
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