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The Number of Subgroups in the Fundamental Groups of Some Non-orientable 3-Manifolds

In: Formal Power Series and Algebraic Combinatorics

Author

Listed:
  • Valery Liskovets

  • Alexander Mednykh

Abstract

The present work supplements our previous enumerative research concerning surfaces and orientable circle bundles over surfaces. We enumerate subgroups of the fundamental groups of non-orientable S 1-bundles over closed surfaces (these bundles are also known as Seifert fiber spaces of types (N,n,I) and (N,o) without exceptional fibers). The results depend on the Euler number of the bundles but they coincide for bundles over non-orientable and orientable surfaces of the same characteristic.

Suggested Citation

  • Valery Liskovets & Alexander Mednykh, 2000. "The Number of Subgroups in the Fundamental Groups of Some Non-orientable 3-Manifolds," Springer Books, in: Daniel Krob & Alexander A. Mikhalev & Alexander V. Mikhalev (ed.), Formal Power Series and Algebraic Combinatorics, pages 276-287, Springer.
    • Handle: RePEc:spr:sprchp:978-3-662-04166-6_25
    DOI: 10.1007/978-3-662-04166-6_25
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