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Non-singular Smale flows on three-dimensional manifolds and Whitehead torsion
Published online by Cambridge University Press: 24 November 2009
Abstract
This paper deals with non-singular Smale flows on oriented 3-manifolds. We shall show a relation between the properties of invariant sets of a Smale flow and a kind of Whitehead torsion of the underlying manifold.
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References
[1]Birman, J. and Williams, R. F.. Knotted periodic orbits in dynamical system II: knot holders for fibered knot. Contemp. Math. 20 (1983), 1–60.CrossRefGoogle Scholar
[2]Bowen, R.. One-dimensional hyperbolic sets for flows. J. Differential Equations 12 (1972), 173–179.CrossRefGoogle Scholar
[3]Bowen, R. and Walters, P.. Expansive one-parameter flows. J. Differential Equations 12 (1972), 180–193.CrossRefGoogle Scholar
[4]Conley, C.. Isolated Invariant Set and the Morse Index (CBMS Regional Conference Series, 38). American Mathematical Society, Providence, RI, 1978.CrossRefGoogle Scholar
[5]Franks, J.. Knots, links and symbolic dynamics. Ann. of Math. (2) 113 (1981), 529–552.CrossRefGoogle Scholar
[6]Franks, J.. Homology and Dynamical Systems (CBMS Regional Conference Series in Mathematics, 49). American Mathematical Society, Providence, RI, 1982, Published for the Conference Board of the Mathematical Sciences, Washington, DC.CrossRefGoogle Scholar
[8]Ghrist, R., Holmes, P. and Sullivan, M.. Knots and Links in Three-Dimensional Flows (Lecture Notes in Mathematics, 1654). Springer, Berlin, 1997.CrossRefGoogle Scholar
[9]Jiang, B. and Wang, S.. Twisted topological invariants associated with representation. Topics in Knot Theory. Ed. Bozhùyùk, M. E.. Kluwer, Dordrecht, 1993, pp. 211–227.CrossRefGoogle Scholar
[10]Milnor, J.. A duality theorem for Reidemeister torsion. Ann. of Math. (2) 76 (1962), 137–147.CrossRefGoogle Scholar
[12]Montgomery, J.. Cohomology of isolated invariant sets under perurbation. J. Differential Equations 13 (1973), 257–299.CrossRefGoogle Scholar
[13]Sánchez-Morgado, H.. Reidemeister torsion and Morse–Smale flows. Ergod. Th. & Dynam. Sys. 16(2) (1996), 405–414.CrossRefGoogle Scholar
[14]Schweitzer, P.. Counterexamples to the Seifert conjecture and opening closed leaves of foliations. Ann. of Math. (2) 100 (1974), 386–400.CrossRefGoogle Scholar
[15]Smale, S.. Differentiable dynamical systems. Bull. Amer. Math. Soc. 73 (1967), 747–817.CrossRefGoogle Scholar
[16]Sullivan, M.. Visually building Smale flows in S 3. Topology Appl. 106(1) (2000), 1–19.CrossRefGoogle Scholar
[17]Turaev, V. G.. Reidemeister torsion in knot theory. Russian Math. Surveys 41(1) (1986), 119–182.CrossRefGoogle Scholar
[18]Wilson, W.. Smoothing derivatives of function and application. Trans. Amer. Math. Soc. 139 (1969), 413–428.CrossRefGoogle Scholar