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Haken spheres for genus two Heegaard splittings

Title
Haken spheres for genus two Heegaard splittings
Author
조상범
Keywords
GOERITZ GROUPS; LENS SPACES; 3-SPHERE; PRESERVE; AUTOMORPHISMS; 3-MANIFOLDS
Issue Date
2017-10
Publisher
CAMBRIDGE UNIV PRESS
Citation
MATHEMATICAL PROCEEDINGS OF THE CAMBRIDGE PHILOSOPHICAL SOCIETY, v. 165, no. 3, page. 563-572
Abstract
A manifold which admits a reducible genus-2 Heegaard splitting is one of the 3-sphere, S-2 x S-1, lens spaces or their connected sums. For each of those splittings, the complex of Haken spheres is defined. When the manifold is the 3-sphere, S-2 x S-1 or a connected sum whose summands are lens spaces or S-2 x S-1, the combinatorial structure of the complex has been studied by several authors. In particular, it was shown that those complexes are all contractible. In this work, we study the remaining cases, that is, when the manifolds are lens spaces. We give a precise description of each of the complexes for the genus-2 Heegaard splittings of lens spaces. A remarkable fact is that the complexes for most lens spaces are not contractible and even not connected.
URI
https://www.cambridge.org/core/journals/mathematical-proceedings-of-the-cambridge-philosophical-society/article/haken-spheres-for-genus-two-heegaard-splittings/F8E51F876A90CFDFBB5CC4CB8A3702F4http://repository.hanyang.ac.kr/handle/20.500.11754/115841
ISSN
0305-0041; 1469-8064
DOI
10.1017/S0305004117000718
Appears in Collections:
COLLEGE OF EDUCATION[S](사범대학) > MATHEMATICS EDUCATION(수학교육과) > Articles
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