What does "Crosscaps" mean?

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Crosscaps are special surfaces in geometry and topology. They are used to study shapes that do not have a clear "inside" or "outside." A common example of a crosscap is the real projective plane, which can be visualized as taking a sphere and creating a twist in one part, connecting opposite points.

In the context of physics, crosscaps are important in the study of two-dimensional conformal field theories (CFTs). These CFTs help describe how particles behave at the smallest scales. When we study CFTs on surfaces with crosscaps, we can learn about their unique properties and behaviors.

Crosscap CFTs are created by adding these non-traditional surfaces to a sphere, which allows for new kinds of interactions and states. The study of crosscaps reveals how these unusual shapes affect the overall physics of a system.

Overall, crosscaps provide a fascinating way to understand complex shapes and their impact on physics and mathematics.