Differential Synthetic Geometry:
A Possible Foundation for a Theory of Gravitation

Craig Spencer, M.S.

Submitted in Partial Fulfillment
of the
Requirements for the Degree
Master of Science

Supervised by

Professor Conrad Plaut
Department of Mathematics, University of Tennessee
Professor Yongli Gao
Department of Physics and Astronomy

The College
Arts and Sciences
University of Rochester
Rochester, New York



An interest in developing a differential version of synthetic geometry is motivated by its potential for gravitational theory, especially a version which might gracefully incorporate spin. This thesis only addresses the needed mathematical foundations; physical applications, if there are any, will have to come later. An axiom set for two dimensions is proposed, some of its consequences explored and, to a certain point, considerable progress is made.

Table of Contents