Noncharacteristic embeddings of the dimensional torus in the dimensional torus
Author:
David Miller
Journal:
Trans. Amer. Math. Soc. 342 (1994), 215240
MSC:
Primary 57Q60; Secondary 57Q35, 57Q45
MathSciNet review:
1179398
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Abstract: We construct certain exotic embeddings of the ntorus in in the standard homotopy class. We turn an embedding characteristic if there exists some map in the standard homotopy class with the property that is the standard coordinate inclusion and . We find examples of noncharacteristic embeddings, f, in dimensions , , and show that these examples are not even cobordant to characteristic embeddings. We let G denote the fundamental group of the complement of the standard coordinate inclusion, . Then we can associate to f a realvalued signature function on the set of jdimensional unitary representations of , where denotes the fundamental group of the localization of with respect to homology with local coefficients in . This function is a cobordism invariant which has certain periodicity properties for characteristic embeddings. We verify that this periodicity does not hold for our examples, f, implying that they are not characteristic. Additional results include a proof that the examples, f, become cobordant to characteristic embeddings upon taking the cartesian product with the identity map on a circle.
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Additional Information
DOI:
http://dx.doi.org/10.1090/S00029947199411793987
PII:
S 00029947(1994)11793987
Article copyright:
© Copyright 1994
American Mathematical Society
