On the cobordisms of Möbius circles

Details On the cobordisms of Möbius circles On the cobordisms of Möbius circles

2006-05-22

arxiv.org/abs/math/0605573v1

Topology Appl. 143 (2004), no. 1-3, 75--85

Mathematics

Geometric Topology

9 pages, 6 figures

Scientific paper

The boundary of a M\"obius manifold carries a canonical M\"obius structure. This enables one to define the cobordism group of $n$-dimensional (closed) M\"obius manifolds. The purpose of this note is to show that the cobordism group of M\"obius circles is zero, i.e., every M\"obius circle bounds a M\"obius surface. We also complete N. Kuiper's classification of projective structures on $S^1$ (we show that there are in fact two series of projective circles with parabolic holonomy, and not one).

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