TO: Alexander Ritter, Associate Professor, University of Oxford, England
FM: Bruce E. Camber
RE: Your work within ArXiv(14) especially with Gabriele Benedetti, Invariance of symplectic cohomology and twisted cotangent bundles over surfaces, 2020, your homepage(s) especially your CV.

 Second email: 23 June 2023

Dear Prof. Dr. Alexander Ritter:

There are 31 references to infinity within your work with G. Benedetti, Invariance of symplectic cohomology and twisted cotangent bundles over surfaces, 2020. Each of those 31 references implies a qualitative relation. Might you have a summary description of those relations? There are also 34 references to different kinds of space. There are multiple references to time-dependents, yet there is no reference to space-time and the assumed values of space-time. What are we to assume about the nature of space-time? Does it have any direct impact on the twisted cotangent bundles? Is it a fair question?

Thank you.

Sincerely,

Bruce

Five of those references to infinity:

• p1: “… the invariant is much richer due to the Hamiltonian dynamics at infinity.”
• p2: “Our paper is concerned with the setup of (typically non-exact) symplectic manifolds which are exact at infinity.”
• p2: “An isomorphism of convex manifolds is a symplectomorphism which preserves the 1-form at infinity.”
• p11: “We must ensure that these trajectories do not escape to infinity so that moduli spaces of Floer trajectories have well-behaved compactifications by broken trajectories.”
• p25: “Explicitly, we twist by any closed two-form β on M exact at infinity.”

First email: 13 September 2022 at 12:55 PM (updated)

Dear Prof. Dr. Alexander Ritter:

Congratulations on your extensive work. I have come to you as a result of your work with Sir Roger. 

Are you familiar with the five-tetrahedral and five-octahedral gaps?

The five-tetrahedral gap is generally associated with Aristotle and his statement about tiling-and-tesselating the universe with tetrahedrons.

I can find no claims to the five-octahedral gap (more images). I believe these gaps might be associated with the geometry of quantum fluctuations so every possible reference is important to me. 

Have you seen any work on that five-octahedral gap?*

Thank you.

Warmly,

Bruce

_____