Some mapping theorems
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- by R. C. Lacher PDF
- Trans. Amer. Math. Soc. 195 (1974), 291-303 Request permission
Abstract:
Various mapping theorems are proved, culminating in the following result for mappings f from a closed $(2k + 1)$-manifold M to another, N: If âalmost allâ point-inverses of f are strongly acyclic in dimensions less than k and if âalmost allâ point-inverses of f have Euler characteristic equal to one, then all but finitely many point-inverses are totally acyclic. (Here âalmost allâ means âexcept on a zero-dimensional set in N".) More can be said when $k = 1$: If f is a monotone map between closed 3-manifolds and if the Euler characteristic of almost-all point-inverses is one, then all but finitely many point-inverses of f are cellular in M; consequently M is the connected sum of N and some other closed 3-manifold and f is homotopic to a spine map. Other results include an acyclicity criterion using the idea of ânonalternatingâ mapping and the following result for PL maps $\phi$ between finite polyhedra X and Y: If the Euler characteristic of each point-inverse of $\phi$ is the integer c then $\chi (X) = c\chi (Y)$.References
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Additional Information
- © Copyright 1974 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 195 (1974), 291-303
- MSC: Primary 57A15
- DOI: https://doi.org/10.1090/S0002-9947-1974-0350743-2
- MathSciNet review: 0350743