One of the effective techniques of mathematics for dealing with problems of several parameters or dimensions is combinatorial, or algebraic, topology. In that field, geometric objects, called cycles, associated to constraints are grouped into deformation or homology classes which then combine and decompose in various combinations to define algebraic structures of such richness to provoke a theoretical study in the own right of a variety of algebraic structures. Recently some of these structures have appeared in theoretical physics in the attempted formalism to describe term by term models for quantum phenomena.
In collaboration, the principal investigator has recently discovered related algebraic topology structures in the space of strings (open and closed) filling up a space (time) model. This award will sponsor investigations to conceptually clarify the occurance of algebraic topology in theoretical quantum physics and to relate the results of these investigations to new string algebra.