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On 4‐Dimensional Mapping Tori and Product Geometries
Author(s) -
Hillman Jonathan A.
Publication year - 1998
Publication title -
journal of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.441
H-Index - 62
eISSN - 1469-7750
pISSN - 0024-6107
DOI - 10.1112/s0024610798006231
Subject(s) - fibration , homotopy , mathematics , torus , pure mathematics , regular homotopy , equivalence (formal languages) , euclidean geometry , homotopy lifting property , n connected , simple (philosophy) , homotopy sphere , product (mathematics) , manifold (fluid mechanics) , topology (electrical circuits) , geometry , combinatorics , engineering , mechanical engineering , philosophy , epistemology
The paper gives simple necessary and sufficient conditions for a closed 4‐manifold to be homotopy equivalent to the mapping torus of a self homotopy equivalence of a PD 3 ‐complex. This is a homotopy analogue of the Stallings and Farrell fibration theorems available in other dimensions. The paper also considers 4‐manifolds which admit a geometry of Euclidean factor type and complex surfaces which fibre over S 1 .
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