## An algebraic classification of certain simple even-dimensional knots

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- by C. Kearton PDF
- Trans. Amer. Math. Soc.
**276**(1983), 1-53 Request permission

## Abstract:

The simple $2q$-knots, $q \geqslant 4$, for which ${H_q}(\tilde {K})$ contains no ${\mathbf {Z}}$-torsion, are classified by means of Hermitian duality pairings on their homology and homotopy modules.## References

- Hyman Bass,
*Algebraic $K$-theory*, W. A. Benjamin, Inc., New York-Amsterdam, 1968. MR**0249491** - Richard C. Blanchfield,
*Intersection theory of manifolds with operators with applications to knot theory*, Ann. of Math. (2)**65**(1957), 340–356. MR**85512**, DOI 10.2307/1969966 - R. H. Fox,
*A quick trip through knot theory*, Topology of 3-manifolds and related topics (Proc. The Univ. of Georgia Institute, 1961) Prentice-Hall, Englewood Cliffs, N.J., 1962, pp. 120–167. MR**0140099** - M. Š. Farber,
*Isotopy types of knots of codimension two*, Trans. Amer. Math. Soc.**261**(1980), no. 1, 185–209. MR**576871**, DOI 10.1090/S0002-9947-1980-0576871-7 - Sze-tsen Hu,
*Homotopy theory*, Pure and Applied Mathematics, Vol. VIII, Academic Press, New York-London, 1959. MR**0106454** - C. Kearton,
*Obstructions to embedding and isotopy in the metastable range*, Math. Ann.**243**(1979), no. 2, 103–113. MR**543720**, DOI 10.1007/BF01420417 - C. Kearton,
*Attempting to classify knot modules and their Hermitian pairings*, Knot theory (Proc. Sem., Plans-sur-Bex, 1977) Lecture Notes in Math., vol. 685, Springer, Berlin, 1978, pp. 227–242. MR**521736** - C. Kearton,
*Presentations of $n$-knots*, Trans. Amer. Math. Soc.**202**(1975), 123–140. MR**358795**, DOI 10.1090/S0002-9947-1975-0358795-1 - C. Kearton,
*Signatures of knots and the free differential calculus*, Quart. J. Math. Oxford Ser. (2)**30**(1979), no. 118, 157–182. MR**534830**, DOI 10.1093/qmath/30.2.157 - C. Kearton,
*Blanchfield duality and simple knots*, Trans. Amer. Math. Soc.**202**(1975), 141–160. MR**358796**, DOI 10.1090/S0002-9947-1975-0358796-3 - C. Kearton,
*An algebraic classification of some even-dimensional knots*, Topology**15**(1976), no. 4, 363–373. MR**442948**, DOI 10.1016/0040-9383(76)90030-6 - C. Kearton and W. B. R. Lickorish,
*Piecewise linear critical levels and collapsing*, Trans. Amer. Math. Soc.**170**(1972), 415–424. MR**310899**, DOI 10.1090/S0002-9947-1972-0310899-2 - Michel A. Kervaire,
*Les nœuds de dimensions supérieures*, Bull. Soc. Math. France**93**(1965), 225–271 (French). MR**189052** - Sadayoshi Kojima,
*A classification of some even dimensional fibered knots*, J. Fac. Sci. Univ. Tokyo Sect. IA Math.**24**(1977), no. 3, 671–683. MR**645407** - Sadayoshi Kojima,
*Classification of simple knots by Levine pairings*, Comment. Math. Helv.**54**(1979), no. 3, 356–367. MR**543336**, DOI 10.1007/BF02566280 - Jerome Levine,
*Knot modules. I*, Trans. Amer. Math. Soc.**229**(1977), 1–50. MR**461518**, DOI 10.1090/S0002-9947-1977-0461518-0 - J. Levine,
*Polynomial invariants of knots of codimension two*, Ann. of Math. (2)**84**(1966), 537–554. MR**200922**, DOI 10.2307/1970459 - J. Levine,
*An algebraic classification of some knots of codimension two*, Comment. Math. Helv.**45**(1970), 185–198. MR**266226**, DOI 10.1007/BF02567325 - Saunders Mac Lane,
*Homology*, Classics in Mathematics, Springer-Verlag, Berlin, 1995. Reprint of the 1975 edition. MR**1344215** - John Milnor,
*Introduction to algebraic $K$-theory*, Annals of Mathematics Studies, No. 72, Princeton University Press, Princeton, N.J.; University of Tokyo Press, Tokyo, 1971. MR**0349811** - D. G. Northcott,
*An introduction to homological algebra*, Cambridge University Press, New York, 1960. MR**0118752**

## Additional Information

- © Copyright 1983 American Mathematical Society
- Journal: Trans. Amer. Math. Soc.
**276**(1983), 1-53 - MSC: Primary 57Q45
- DOI: https://doi.org/10.1090/S0002-9947-1983-0684492-3
- MathSciNet review: 684492