ON THE CONNECTIVITY OF THE BRANCH LOCUS OF THE SCHOTTKY SPACE
2014 (English)In: Annales Academiae Scientiarum Fennicae Mathematica, ISSN 1239-629X, E-ISSN 1798-2383, Vol. 39, no 2, 635-654 p.Article in journal (Refereed) Published
Let M be a handlebody of genus g greater than= 2. The space T(M), that parametrizes marked Kleinian structures on M up to isomorphisms, can be identified with the space MSg, of marked Schottky groups of rank g, so it carries a structure of complex manifold of finite dimension 3(g - 1). The space M(M) parametrizing Kleinian structures on M up to isomorphisms, can be identified with S-g, the Schottky space of rank g, and it carries the structure of a complex orbifold. In these identifications, the projection map pi: T(M) -greater than M(M) corresponds to the map from MSg, onto S-g that forgets the marking. In this paper we observe that the singular locus B(M) of M(M), that is, the branch locus of pi, has (i) exactly two connected components for g = 2, (ii) at most two connected components for g greater than= 4 even, and (iii) M(M) is connected for g greater than= 3 odd.
Place, publisher, year, edition, pages
Suomalainen Tiedeakatemia (Finnish Academy of Science and Letters) / Academia Scientiarum Fennica , 2014. Vol. 39, no 2, 635-654 p.
Moduli space; branch locus; Schottky space; Schottky group; handlebody; Riemann surface; Kleinian group; Fuchsian group
IdentifiersURN: urn:nbn:se:liu:diva-109890DOI: 10.5186/aasfm.2014.3942ISI: 000340017600011OAI: oai:DiVA.org:liu-109890DiVA: diva2:741552
Funding Agencies|UTFSM [12.13.01]; [Fondecyt 1110001]2014-08-282014-08-282015-03-09