21. Orientable surfaces can be visualized, and their diffeomorphism classes enumerated, by genus. 22. Unfortunately, this theory is not diffeomorphism covariant. 23. Composing these diffeomorphisms gives a diffeomorphism carrying the smooth curve onto the unit circle. 24. In that case one of the homeomorphisms can be chosen to be a diffeomorphism . 25. On the other hand, the right hand side is imdependent of the diffeomorphism . 26. A diffeomorphism between two symplectic manifolds which preserves the symplectic form is called a symplectomorphism. 27. To handle the spatial diffeomorphism constraint we need to go over to the loop representation. 28. The spatial diffeomorphism constraint has been solved. 29. Both gauge invariance and diffeomorphism invariance reflect a redundancy in the description of the system. 30. This means that one cannot just solve the spatial diffeomorphism constraint and then the Hamiltonian constraint.
