Geometrical morphology

This is a working paper, describing work that the two of us have done over the course of 2016 and the beginning of 2017, developing in some detail an analysis of some aspects of inflectional morphology. In most respects this work continues the development of work in this area over the past fifty or more years, but in one or two important ways our approach is different. We believe that a geometric interpretation of inflectional morphology is possible, and that it simplifies our understanding of the formal aspects of the syntax-morphology interface. It simplifies our understanding in that renders unnecessary a large part of the derivational mechanics that have been part and parcel of most formalisms in this area. Readers for whom the mathematics below is unfamiliar are unlikely to agree with us that this is a simplification, but we will do our best to show that the mathematics and the geometry that we exploit is quite helpful in expressing our ideas about how languages work. Here is a list of some central ideas, to get us started: