Some mapping theorems
Author:
R. C. Lacher
Journal:
Trans. Amer. Math. Soc. 195 (1974), 291303
MSC:
Primary 57A15
MathSciNet review:
0350743
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Abstract: Various mapping theorems are proved, culminating in the following result for mappings f from a closed manifold M to another, N: If ``almost all'' pointinverses of f are strongly acyclic in dimensions less than k and if ``almost all'' pointinverses of f have Euler characteristic equal to one, then all but finitely many pointinverses are totally acyclic. (Here ``almost all'' means ``except on a zerodimensional set in N".) More can be said when : If f is a monotone map between closed 3manifolds and if the Euler characteristic of almostall pointinverses is one, then all but finitely many pointinverses of f are cellular in M; consequently M is the connected sum of N and some other closed 3manifold and f is homotopic to a spine map. Other results include an acyclicity criterion using the idea of ``nonalternating'' mapping and the following result for PL maps between finite polyhedra X and Y: If the Euler characteristic of each pointinverse of is the integer c then .
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Additional Information
DOI:
http://dx.doi.org/10.1090/S00029947197403507432
PII:
S 00029947(1974)03507432
Keywords:
Mapping,
acyclic,
finiteness,
cellularity
Article copyright:
© Copyright 1974 American Mathematical Society
