The concordance diffeomorphism group of real projective space
Author:
Robert Wells
Journal:
Trans. Amer. Math. Soc. 192 (1974), 319337
MSC:
Primary 57D50
MathSciNet review:
0339224
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Abstract: Let be rdimensional real projective space with r odd, and let be the group of orientation preserving diffeomorphisms factored by the normal subgroup of those concordant (= pseudoisotopic) to the identity. The main theorem of this paper is that for the group is isomorphic to the homotopy group , where with and . The function is denned by . The theorem is proved by introducing a cobordism version of the mapping torus construction; this mapping torus construction is a homomorphism for and a suitable Lashof cobordism group. It is shown that t is an isomorphism onto the torsion subgroup , and that this subgroup is isomorphic to as above. Then one reads off from Mahowald's tables of that and .
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Additional Information
DOI:
http://dx.doi.org/10.1090/S0002994719740339224X
PII:
S 00029947(1974)0339224X
Keywords:
Diffeomorphism,
concordance,
pseudoisotopy,
Lashof cobordism groups,
MoorePostnikov decomposition,
mapping torus,
surgery,
Wall groups
Article copyright:
© Copyright 1974
American Mathematical Society
