Remote Access Transactions of the American Mathematical Society
Green Open Access

Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 
 

 

Diffeomorphic invariants of immersed circles


Author: Roger F. Verhey
Journal: Trans. Amer. Math. Soc. 163 (1972), 47-63
MSC: Primary 57.20; Secondary 30.00
DOI: https://doi.org/10.1090/S0002-9947-1972-0286122-4
MathSciNet review: 0286122
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: The intersection sequences of a normal immersion form a complete invariant for diffeomorphically equivalent normal immersions. Numerical invariants and inequalities on numerical invariants are obtained using intersection sequences.


References [Enhancements On Off] (What's this?)

  • [1] G. K. Francis, Null genus realizability criterion for abstract intersection sequences, J. Combinatorial Theory 7 (1969), 331-341. MR 40 #5475. MR 0252254 (40:5475)
  • [2] -, The folded ribbon theorem. A contribution to the study of immersed circles, Trans. Amer. Math. Soc. 141 (1969), 271-303. MR 39 #4863. MR 0243542 (39:4863)
  • [3] Charles Loewner, A topological characterization of a class of integral operators, Ann. of Math. (2) 49 (1948), 316-332. MR 9, 502. MR 0024487 (9:502d)
  • [4] C. J. Titus, A theory of normal curves and some applications, Pacific J. Math. 10 (1960), 1083-1096. MR 22 #5014. MR 0114189 (22:5014)
  • [5] T. Umezawa, On the theory of Univalent functions, Tôhoku Math. J. (2) 7 (1955), 212-228. MR 17, 1068. MR 0077630 (17:1068h)
  • [6] Hassler Whitney, On regular closed curves in the plane, Compositio Math. 4 (1937), 276-284. MR 1556973

Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 57.20, 30.00

Retrieve articles in all journals with MSC: 57.20, 30.00


Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1972-0286122-4
Keywords: Normal immersion, intersection sequence, diffeomorphically equivalent, complete invariant, numerical invariant, winding number, tangent winding number, total variation
Article copyright: © Copyright 1972 American Mathematical Society

American Mathematical Society