Representing characteristic homology classes of
Authors:
Jian Han Guo and Dan Yan Gan
Journal:
Proc. Amer. Math. Soc. 121 (1994), 12511255
MSC:
Primary 57R95; Secondary 57R40
MathSciNet review:
1205494
Fulltext PDF Free Access
Abstract 
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Abstract: We prove the following theorems. Theorem 1. If is a characteristic homology class with and (1) provided , or (2) provided . Suppose that the 11/8conjecture is true. Then x cannot be represented by a smoothly embedded 2sphere. Theorem 2. Let be a primitive characteristic homology class with . Then x can be represented by a smoothly embedded 2sphere.
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 , Embeddings and immersions of a 2sphere in 4manifolds, Proc. Amer. Math. Soc. 118 (1993), 13231330. MR 1152976 (93j:57018)
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 R. E. Gompf, Infinite families of Casson handles and topological disks, Topology 23 (1984), 395400. MR 780732 (86i:57040)
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 M. Kervaire and J. Milnor, On 2spheres in 4manifolds, Proc. Nat. Acad. Sci. U.S.A. 47 (1961), 16511657. MR 0133134 (24:A2968)
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 K. Kuga, Representing homology classes of , Topology 23 (1984), 133137. MR 744845 (85m:57011)
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 T. Lawson, Representing homology classes of almost definite 4manifolds, Michigan Math. J. 34 (1987), 8591. MR 873022 (88d:57024)
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 B. H. Li, Embeddings of surfaces in 4manifolds (I), Chinese Sci. Bull. 36 (1991), 20252029. MR 1150851 (93d:57037)
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 F. Luo, Representing homology classes in , Pacific J. Math. 133 (1988), 137140. MR 936360 (89h:57031)
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 C. T. C. Wall, On the orthogonal groups of unimodular quadratic forms, Math. Ann. 149 (1962), 328338. MR 0138565 (25:2009)
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 , Diffeomorphisms of 4manifolds, J. London Math. Soc. 39 (1964), 131140. MR 0163323 (29:626)
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Additional Information
DOI:
http://dx.doi.org/10.1090/S00029939199412054947
PII:
S 00029939(1994)12054947
Keywords:
Representing,
characteristic homology class,
primitive
Article copyright:
© Copyright 1994
American Mathematical Society
