# What is Topology?

Topology is a field of study that investigates the invariant properties that remain after continuous deformation of a structure. Topology originated as a branch of mathematics and has played an important role in the development of the general theory of relativity and quantum theory, which represent 20th century physics. We believe that the concept of topology can be helpful in understanding phenomena in modern materials science, complex system science, networks of life, economics, and information science from a broader perspective. This program aims to explore complex phenomena in various scientific fields (multi-degree-of-freedom, non-equilibrium, non-linear, hierarchical structure) from a topological perspective. Our studies will be based on the results of original research performed by our members, e.g., the discoveries of (a) Möbius crystals, (b) slime mold (myxomycete) network intelligence, and (c) a new order of topological defects, and verification of fractons. Our ultimate goal is to create an innovative field, topological science and technology, which will pursue the discovery of new natural phenomena and laws as well as the development of new technologies.

## Our four projects:

B. Topology in relation to critical phenomena