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Enumeration of subgroups in the fundamental groups of orientable circle bundles over surfaces

 

作者: Valery Liskovets,   Alexander Mednykh,  

 

期刊: Communications in Algebra  （Taylor Available online 2000）
卷期: Volume 28, issue 4  

页码: 1717-1738

 

ISSN:0092-7872

 

年代: 2000

 

DOI:10.1080/00927870008826924

 

出版商: Gordon and Breach Science Publishers Ltd.

 

关键词: Seifert fibre space;S1-bundle;Euler number;3-manifold;surface group;covering;fundamental group;transitive permutational

 

数据来源: Taylor

 

摘要:

The aim of this paper is to count subgroups of a given index in the fundamental group of an orientableS1-bundle over a compact surface. The number of subgroups of indexnturns out to be independent of the orientability of the base surface 𝔣, closed or bordered, and is expressed as a linear combination of the numbers of surface subgroups of indicesm = n/ll∣n. For a closed base surface of characteristic χ the respective coefficients are equal tol–χm+2or vanish depending onl,nand the Euler number of theS1-bundle.

 

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