It wouldn't seems so to me since the universal cover is basically the space of all paths from the identity to various points, since the orthogonal group has two connected components wouldn't it be impossible to define paths from the identity to the other component of the group, making it impossible to define a universal cover? Its not that I read anywhere that the Pin group is the universal cover I just want to double check.
2026-03-28 06:59:57.1774681197
Is the Spin group the universal cover of the orthogonal group?
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