A new construction of lens spaces

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Let T-n be the real n-torus group. We introduce a new definition of lens spaces and give some sufficient conditions for diffeomorphic classification of lens spaces. We show that any 3-dimensional lens space L(p; q) is T-2-equivariantly cobordant to zero. We also give some sufficient conditions for higher dimensional lens spaces L(p; q(1), ..., q(n)) to be Tn+1-equivariantly cobordant to zero. General results in equivariant topology imply that torus equivariant complex bordism classes of lens spaces are trivial. In contrast, our proofs are constructive using toric topological arguments. (C) 2018 Elsevier B.V. All rights reserved.
Publisher
ELSEVIER SCIENCE BV
Issue Date
2018-05
Language
English
Article Type
Article
Keywords

ORBIFOLDS; TORUS; 4-MANIFOLDS; BORDISM

Citation

TOPOLOGY AND ITS APPLICATIONS, v.240, pp.1 - 20

ISSN
0166-8641
DOI
10.1016/j.topol.2018.02.032
URI
http://hdl.handle.net/10203/242335
Appears in Collection
MA-Journal Papers(저널논문)
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