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Coincidence classes in nonorientable manifolds


We study Nielsen coincidence theory for maps between manifolds of same dimension regardless of orientation. We use the definition of semi-index of a class, review the definition of defective classes, and study the occurrence of defective root classes. We prove a semi-index product formula for lifting maps and give conditions for the defective coincidence classes to be the only essential classes.



  1. Brown RF, Schirmer H: Nielsen root theory and Hopf degree theory. Pacific Journal of Mathematics 2001,198(1):49–80. 10.2140/pjm.2001.198.49

    Article  MathSciNet  MATH  Google Scholar 

  2. Dobreńko R, Jezierski J: The coincidence Nielsen number on nonorientable manifolds. The Rocky Mountain Journal of Mathematics 1993,23(1):67–85. 10.1216/rmjm/1181072611

    Article  MathSciNet  MATH  Google Scholar 

  3. Gonçalves DL, Wong PN-S: Homogeneous spaces in coincidence theory. Matemática Contemporânea 1997, 13: 143–158. 10th Brazilian Topology Meeting (São Carlos, 1996), (P. Schweitzer, ed.), Sociedade Brasileira de Matemática

    MathSciNet  MATH  Google Scholar 

  4. Gonçalves DL, Wong PN-S: Nilmanifolds are {J}iang-type spaces for coincidences. Forum Mathematicum 2001,13(1):133–141. 10.1515/form.2001.002

    Article  MathSciNet  MATH  Google Scholar 

  5. Jezierski J: The semi-index product formula. Polska Akademia Nauk. Fundamenta Mathematicae 1992,140(2):99–120.

    MathSciNet  MATH  Google Scholar 

  6. Jezierski J: The Nielsen coincidence theory on topological manifolds. Fundamenta Mathematicae 1993,143(2):167–178.

    MathSciNet  MATH  Google Scholar 

  7. Olum P: Mappings of manifolds and the notion of degree. Annals of Mathematics. Second Series 1953, 58: 458–480. 10.2307/1969748

    Article  MathSciNet  MATH  Google Scholar 

  8. Skora R: The degree of a map between surfaces. Mathematische Annalen 1987,276(3):415–423. 10.1007/BF01450838

    Article  MathSciNet  MATH  Google Scholar 

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Correspondence to Daniel Vendrúscolo.

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Open Access This article is distributed under the terms of the Creative Commons Attribution 2.0 International License ( ), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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Vendrúscolo, D. Coincidence classes in nonorientable manifolds. Fixed Point Theory Appl 2006, 68513 (2006).

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