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Original Articles

Embeddings of 3-Manifolds in S4 from the Point of View of the 11-Tetrahedron Census

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References

  • Agol, I. (2000). Bounds on exceptional Dehn filling. Geom. Topol. 4: 431–449. DOI: 10.2140/gt.2000.4.431
  • Agol, I., Freedman, M. (2019) Embedding Heegaard decompositions. arXiv. 1906.03244. In press.
  • Akbulut, S., Kirby, R. (1979). Mazur manifolds. Michigan Math. J. 26: 259–284. DOI: 10.1307/mmj/1029002261
  • Bott, R. (1954). Nondegenerate critical manifolds. Ann. Math. 60(2): 248–261. DOI: 10.2307/1969631
  • Budney, R. (2008). A family of embedding spaces. Geom. Topol. Monogr. 13: 41–83. DOI: 10.2140/gtm.2008.13.41
  • Burton, B., Budney, R., Pettersson, W., et al. (1999–2020). Regina: Software for 3-manifold topology and normal surface theory [http://regina.sourceforge.net/].
  • Callahan, P. J., Hildebrand, J. C., Weeks, J. R. (1999). A census of cusped hyperbolic 3-manifolds. Math. Comput. 68(225): 321–333. DOI: 10.1090/S0025-5718-99-01036-4
  • Casson, A., Harer, J. (1981). Some homology lens spaces which bound rational homology balls. Pacific J. Math. 96(1): 23–36. DOI: 10.2140/pjm.1981.96.23
  • Cerf, J. (1968). Sur les Difféomorphismes de la Sphère de Dimension Trois (Γ4 = 0), Lecture Notes in Mathematics, No. 53. Berlin-New York: Springer-Verlag.
  • Cha, J. C., Livingston, C. (2018). Unknown values in the table of knots. arXiv [math.GT/0503125]. In press.
  • Costantino, F., Thurston, D. (2008). 3-manifolds efficiently bound 4-manifolds. J. Topol. 1(3): 703–745. arXiv [math.GT/0506577]. DOI: 10.1112/jtopol/jtn017
  • Crisp, J. S., Hillman, J. A. (1998). Embedding Seifert fibred 3-manifolds and Sol3 -manifolds in 4-space. Proc. Lond. Math. Soc. 76(3): 685–710. DOI: 10.1112/S0024611598000379
  • Culler, M., Gordon, C., Luecke, J., Shalen, P. (1987). Dehn surgery on knots. Ann. Math. 125(2): 237–300. DOI: 10.2307/1971311
  • Donald, A. (2014). Embedding Seifert manifolds in S4. Trans. Amer. Math. Soc. 367(1): 559–595. [arXiv:1203.6008]. DOI: 10.1090/S0002-9947-2014-06174-6
  • Dranisnikov, A., Repovs, D. (1993). Embeddings up to homotopy type in Euclidean Space. Bull. Austral. Math. Soc. 47(1):145--148. DOI: 10.1017/S0004972700012338
  • Epstein, D. B. A. (1965). Embedding punctured manifolds. Proc. Amer. Math. Soc. 16(2): 175–176. DOI: 10.1090/S0002-9939-1965-0208606-9
  • Erle, D. (1969). Die quadratische form eines knotens, und ein Satz über Knotenmannigfaltigkeiten. J. Reine Angew. Math. 236: 174–218.
  • Fickle, H. (1984). Knots, Z-homology 3-spheres and contractible 4-manifolds. Houston J. Math. 10(4): 467–493.
  • Fintushel, R., Stern, R. (1987). Rational homology cobordisms of spherical space forms. Topology 26(3): 385–393. DOI: 10.1016/0040-9383(87)90008-5
  • Gilmer, P. M., Livingston, C. (1983). On embedding 3-manifolds in 4-space. Topology 22(3): 241–252. DOI: 10.1016/0040-9383(83)90011-3
  • Gompf, R., Stipsicz, A. (1999). 4-manifolds and kirby calculus. Graduate Stud. Math. 20:1–558.
  • Hantzsche, W. (1938). Einlagerung von Mannigflitigkeiten in euklidishe Raume. Math. Z. 43(1): 38–58. DOI: 10.1007/BF01181085
  • Hillman, J. A. Algebraic Invariants of Links, Series on Knots and Everything, Vol. 32. World Scientific. World Scientific Publishing Co Pte Ltd, 5 Toh Tuck Link, Singapore 596224.
  • Hillman, J. A. Embedding 3-manifolds with circle actions in 4-space. Proc. AMS. In press. [http://www.maths.usyd.edu.au/u/pubs/publist/preprints/2008/hillman-19.html]
  • Issa, A., McCoy, D. (2018) Smoothly embedding Seifert fibered spaces in S4. arXiv [1810.04770]. In press.
  • Jänich, K., Ossa, E. (1969). On the signature of an involution. Topology 8(1): 27–30. DOI: 10.1016/0040-9383(69)90027-5
  • Kawauchi, A. (1977). On quadratic forms of 3-manifolds. Invent. Math. 43(2): 177–198. DOI: 10.1007/BF01390003
  • Kawauchi, A., Kojima, S. (1980). Algebraic classification of linking pairings on 3-manifolds. Math. Ann. 253(1): 29–42. DOI: 10.1007/BF01457818
  • Kearton, C. (1979). Signatures of knots and the free differential calculus. Q. J. Math. 30(2): 157–182. DOI: 10.1093/qmath/30.2.157
  • Kirby, R. (1374). The Topology of 4-Manifolds. Tiergartenstrasse 17, D-69121 Heidelberg Germany.
  • Kosinski, A. (1993). Differential Manifolds. Academic Press; Vol. 138 Pure and Applied Mathematics. Dover Publications (October 19, 2007).
  • Kronheimer, P., Mrowka, T. (2007). Monopoles and Three-Manifolds. University Printing House, Shaftesbury Road, Cambridge, CB2 8BS, United Kingdom.
  • Lisca, P. (2007). Sums of lens spaces bounding rational balls. Algebr. Geom. Topol. 7: 2141–2164. DOI: 10.2140/agt.2007.7.2141
  • Litherland, R. A. (1979). Deforming twist-spun knots. Trans. Amer. Math. Soc. 250: 311–331. DOI: 10.1090/S0002-9947-1979-0530058-4
  • Livingston, C. (2005). A Survey of Classical Knot Concordance, Handbook of Knot Theory. Radarweg 29, 1043 NX Amsterdam, The Netherlands, pp. 319–347.
  • Massey, W. S. (1969). Proof of a conjecture of Whitney. Pacific J. Math. 31(1): 143–156. DOI: 10.2140/pjm.1969.31.143
  • Matveev, S. V. (2005). Recognition and tabulation of three-dimensional manifolds. Dokl. Akad. Nauk 400(1): 26–28.
  • Mijatovic, A. (2005). Simplicial structures of knot complements. Math. Res. Lett. 12(6): 843–856. DOI: 10.4310/MRL.2005.v12.n6.a6
  • Milnor, J. (1963). Spin structures on manifolds. L’enseignement Mathématique 9: 198–203.
  • Milnor, J., Stasheff, J. (1974). Characteristic Classes. Princeton University Press.
  • Orlik, P. (1972). Seifert manifolds Lecture Notes in Mathematics, Vol. 291. Tiergartenstrasse 17, D-69121 Heidelberg Germany.
  • Oszváth, P., Szabó, Z. (2003). Absolutely graded Floer homologies and intersection forms for four-manifolds with boundary. Adv. Math. 173: 225–254.
  • Ruberman, D. (1990). Seifert surfaces of knots in S4. Pacific J. Math. 145(1): 97–116. DOI: 10.2140/pjm.1990.145.97
  • Saveliev, N. (2002). Invariants for Homology 3-Spheres. Encyclopedia of Mathematical Sciences, Vol. 140. Tiergartenstrasse 17, D-69121 Heidelberg Germany.
  • Schubert, H. (1953). Knoten und vollringe. Acta Math. 90: 131–286. DOI: 10.1007/BF02392437
  • Seifert, H., Threlfall, W. (1980). Seifert and Threlfall’s Textbook of Topology. Radarweg 29, 1043 NX Amsterdam, The Netherlands Academic Press.
  • Siebenmann, L. (1980). On Vanishing of the Rohlin Invariant and Nonfinitely Amphicheiral Homology 3-Spheres Topology Symposium, Siegen 1979, Lecture Notes in Mathematics, Vol. 788. Tiergartenstrasse 17, D-69121 Heidelberg Germany, pp. 172–222.
  • Skopenkov, A. (2008). Classification of smooth embeddings of 3-manifolds in the 6-space. Math. Z. 260(3): 647–672. DOI: 10.1007/s00209-007-0294-1
  • Stern, R. (1978). Some Brieskorn spheres which bound contractible manifolds. Notices Amer. Math. Soc. 25(A448): 313–317.
  • Taylor, L. (2005). Complex Spin structures on 3-manifolds. Fields Institute Commun. 47: 313–317.
  • The knot atlas [http://katlas.org]
  • Trotter, H. (1973). On s-equivalence of Seifert matrices. Invent. Math. 20(3): 173–207. DOI: 10.1007/BF01394094
  • Wall, C. T. C. (1965). All 3-manifolds imbed in 5-space. Bull. Amer. Math. Soc. 71(3): 564–567. DOI: 10.1090/S0002-9904-1965-11332-5
  • Whitney, H. (1941). On the Topology of Differentiable Manifolds, Lectures in Topology. 839 Greene Street, Ann Arbor, MI: University of Michigan Press, pp. 101–141.

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