Real Spinorial Groups by Sebastià Xambó-Descamps

Author:Sebastià Xambó-Descamps
Language: eng
Format: epub
ISBN: 9783030004040
Publisher: Springer International Publishing

and is the reflection along the direction v = ue iθ, for −vvv −1 = −v. Thus, we see that topologically is the disjoint union of two circles: and . The 2:1 map is manifested in the fact that v and −v give the same reflection. In other words, topologically is also a circle that is circled twice when going once around the circle uU 1 (see Fig. 5.3).

Fig. 5.3Fix the vector u, say u = e 1. The circle uU 1 ⊂ E 2 provides a 2:1 representation of the set of reflections of E 2, as is the reflection along v, or across the line v ⊥, and ±v yield the same reflection

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