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Heegaard splittings, the virtually Haken conjecture and Property tau

Abstract:

We examine three key conjectures in 3-manifold theory: the virtually Haken conjecture, the positive virtual b_1 conjecture and the virtually fibred conjecture. We explore the interaction of these conjectures with the following seemingly unrelated areas: eigenvalues of the Laplacian, and Heegaard splittings. We first give a necessary and sufficient condition, in terms of spectral geometry, for a finitely presented group to have a finite index subgroup with infinite abelianisation. For negati...

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Publication status:
Published

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Publisher copy:
10.1007/s00222-005-0480-x

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Institution:
University of Oxford
Department:
Oxford, MPLS, Mathematical Inst
Journal:
INVENTIONES MATHEMATICAE
Volume:
164
Issue:
2
Pages:
317-359
Publication date:
2002-05-31
DOI:
EISSN:
1432-1297
ISSN:
0020-9910
URN:
uuid:94e9501e-18da-467a-b420-a641a5645a48
Source identifiers:
30663
Local pid:
pubs:30663

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