On a $4$-manifold homology equivalent to a bouquet of surfaces
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- by Akio Kawauchi PDF
- Trans. Amer. Math. Soc. 262 (1980), 95-112 Request permission
Abstract:
This paper gives some algebraic invariants for a piecewise linear imbedding of a surface into some 4-manifold inducing a Z or Q-homology isomorphism. Several examples are obtained by using these invariants.References
- Sylvain E. Cappell and Julius Shaneson, Totally spineless manifolds, Illinois J. Math. 21 (1977), no. 2, 231–239. MR 442946 W. T. Eaton, C. P. Pixley and G. A. Venema, A topological embedding which cannot be approximated by a piecewise linear embedding, Notices Amer. Math. Soc. 24 (1977), A-302.
- Ralph H. Fox and John W. Milnor, Singularities of $2$-spheres in $4$-space and cobordism of knots, Osaka Math. J. 3 (1966), 257–267. MR 211392 C. H. Giffen, Disciplining dunce hats in 4-manifolds (preprint).
- Mitsuyoshi Kato, Embedding spheres and balls in codimension $\leq 2$, Invent. Math. 10 (1970), 89–107. MR 270379, DOI 10.1007/BF01403149
- Akio Kawauchi, On links not cobordant to split links, Topology 19 (1980), no. 4, 321–334. MR 584558, DOI 10.1016/0040-9383(80)90017-8
- Akio Kawauchi, A partial Poincaré duality theorem for infinite cyclic coverings, Quart. J. Math. Oxford Ser. (2) 26 (1975), no. 104, 437–458. MR 394691, DOI 10.1093/qmath/26.1.437
- Akio Kawauchi, $H$-cobordism. I. The groups among three dimensional homology handles, Osaka Math. J. 13 (1976), no. 3, 567–590. MR 433474
- Akio Kawauchi, On quadratic forms of $3$-manifolds, Invent. Math. 43 (1977), no. 2, 177–198. MR 488074, DOI 10.1007/BF01390003
- Akio Kawauchi, On the Alexander polynomials of cobordant links, Osaka Math. J. 15 (1978), no. 1, 151–159. MR 488022
- Akio Kawauchi, Three dimensional homology handles and circles, Osaka Math. J. 12 (1975), no. 3, 565–581. MR 391110 —, Imbedding problem of 3-manifolds into 4-manifolds (in preparation).
- Howard Lambert, A class of nonsplittable links, Michigan Math. J. 24 (1977), no. 1, 45–50. MR 482738
- J. Levine, Invariants of knot cobordism, Invent. Math. 8 (1969), 98–110; addendum, ibid. 8 (1969), 355. MR 253348, DOI 10.1007/BF01404613
- Yukio Matsumoto, A $4$-manifold which admits no spine, Bull. Amer. Math. Soc. 81 (1975), 467–470. MR 380814, DOI 10.1090/S0002-9904-1975-13787-6
- Yukio Matsumoto, Some counterexamples in the theory of embedding manifolds in codimension two, Sci. Papers College Gen. Ed. Univ. Tokyo 25 (1975), no. 2, 49–57. MR 397745 —, Secondary intersectional properties of 4-manifolds and Whitney’s trick, Proc. Sympos. Pure Math., vol. 32, Amer. Math. Soc., Providence, R. I., 1978, pp. 99-107. —, Wild embeddings of piecewise linear manifolds in codimension two (preprint).
- John W. Milnor, Infinite cyclic coverings, Conference on the Topology of Manifolds (Michigan State Univ., E. Lansing, Mich., 1967) Prindle, Weber & Schmidt, Boston, Mass., 1968, pp. 115–133. MR 0242163
- John Milnor, On isometries of inner product spaces, Invent. Math. 8 (1969), 83–97. MR 249519, DOI 10.1007/BF01404612
- Kunio Murasugi, On a certain numerical invariant of link types, Trans. Amer. Math. Soc. 117 (1965), 387–422. MR 171275, DOI 10.1090/S0002-9947-1965-0171275-5 N. Smythe, Boundary links, Topology Seminar, Wisconsin, 1965, Ann. Math. Studies, no. 60, Princeton Univ. Press, Princeton, N. J., 1966, pp. 69-72.
Additional Information
- © Copyright 1980 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 262 (1980), 95-112
- MSC: Primary 57Q35; Secondary 57M99
- DOI: https://doi.org/10.1090/S0002-9947-1980-0583848-4
- MathSciNet review: 583848