caa a22 4500 445884231 CHVBK 20180317145554.0 cr unu---uuuuu 170323e20110401xx s 000 0 eng 10.1007/s10711-010-9531-6 doi (NATIONALLICENCE)springer-10.1007/s10711-010-9531-6 Gongopadhyay Krishnendu Mathematics, Indian Institute of Science Education and Research (IISER) Mohali, Transit Campus: MGSIPAP Complex, Sector 26, 160019, Chandigarh, India aut Conjugacy classes in Möbius groups [Elektronische Daten] [Krishnendu Gongopadhyay] Let $${\mathbb H^{n+1}}$$ denote the n + 1-dimensional (real) hyperbolic space. Let $${\mathbb {S}^{n}}$$ denote the conformal boundary of the hyperbolic space. The group of conformal diffeomorphisms of $${\mathbb {S}^{n}}$$ is denoted by M(n). Let M o(n) be its identity component which consists of all orientation-preserving elements in M(n). The conjugacy classification of isometries in M o(n) depends on the conjugacy of T and T −1 in M o(n). For an element T in M(n), T and T −1 are conjugate in M(n), but they may not be conjugate in M o(n). In the literature, T is called real if T is conjugate in M o(n) to T −1. In this paper we classify real elements in M o(n). Let T be an element in M o(n). Corresponding to T there is an associated element T o in SO(n+1). If the complex conjugate eigenvalues of T o are given by $${\{e^{i\theta_j}, e^{-i\theta_j}\}, 0 < \theta_j \leq \pi, j=1,\ldots,k}$$ , then {θ1, . . . , θk} are called the rotation angles of T. If the rotation angles of T are distinct from each-other, then T is called a regular element. After classifying the real elements in M o(n) we have parametrized the conjugacy classes of regular elements in M o(n). In the parametrization, when T is not conjugate to T −1 , we have enlarged the group and have considered the conjugacy class of T in M(n). We prove that each such conjugacy class can be induced with a fibration structure. Springer Science+Business Media B.V., 2010 Hyperbolic space nationallicence Möbius groups nationallicence Conjugacy classes nationallicence Real elements nationallicence Geometriae Dedicata Springer Netherlands 151/1(2011-04-01), 245-258 0046-5755 151:1<245 2011 151 10711 https://doi.org/10.1007/s10711-010-9531-6 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s10711-010-9531-6 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Gongopadhyay Krishnendu Mathematics, Indian Institute of Science Education and Research (IISER) Mohali, Transit Campus: MGSIPAP Complex, Sector 26, 160019, Chandigarh, India aut NATIONALLICENCE 773 0- Geometriae Dedicata Springer Netherlands 151/1(2011-04-01), 245-258 0046-5755 151:1<245 2011 151 10711 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer