Curved Spaces Icon Curved Spaces

Curved Spaces screenshot

Curved Spaces is a flight simulator for multiconnected universes. Such toy universes are the 3D analog of the torus and Klein bottle on which the simpler 2D Torus Games are played. Because light itself wraps around such a space, inhabitants see their universe’s contents repeating in a crystalline pattern, like a hall of mirrors but with no reflection.

Curved Spaces is intended for undergraduates and graduate students studying 3‑manifolds, and has also found use as a research tool in topology and cosmology.

English, Spanish, French, Japanese, Chinese (simplified), Chinese (traditional)
Last update
26 April 2018 (Version 3.7.2)
(Mac) Minor changes for macOS 10.13

Contact Jeff Weeks.

With deepest thanks to the translators for their thorough, careful and most professional translation of Curved Spaces:
Alberto Pino Blanco, Roland Lehoucq, 竹内建 (Tatsu Takeuchi), 邹燕清 (Yanqing Zou).

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This material is based upon work supported by the National Science Foundation under Grant No. 1503701. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author and do not necessarily reflect the views of the National Science Foundation.

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