The Wecken problem for coincidences of boundary preserving surface maps
DOI:
https://doi.org/10.12775/TMNA.2022.061Słowa kluczowe
Boundary preserving map, coincidence point, Wecken problemAbstrakt
We prove a Brooks type coincidence minimization result for boundary preserving maps on compact surfaces with boundary. As an application we obtain non-boundary Wecken results for pairs of maps $f,g\colon (X,\partial X) \to (X,\partial X)$ for most surfaces $X$.Bibliografia
R. Brooks, On removing coincidences of two maps when only one, rather than both, of them may be deformed by a homotopy, Pacific J. Math. 40 (1972), 45–52.
R.F. Brown and M.R. Kelly, The boundary-Wecken classification of surfaces, Algebr. Geom. Topol. 4 (2004), 49–71.
R.F. Brown and B.J. Sanderson, Fixed points of boundary-preserving maps of surfaces, Pacific J. Math. 158 (1993), 243–264.
D.B.A. Epstein, Curves on 2-manifolds and isotopies, Acta Math. 115 (1966), 83–107.
D.L. Gonçalves, Coincidence theory, Handbook of Topological Fixed Point Theory, Springer, Dordrecht, 2005, pp. 3-42.
D.L. Gonçalves, Coincidence of maps between surfaces, J. Korean Math. Soc. 36 (1999), 243–256.
D.L. Gonçalves and T. Nasybullov, Explicit solution of certain orientable quadratic equations in fre groups, International J. Algebra Comput. 29 (2019), no. 8, 1451–1466.
C.G. Jang and S. Lee, A relative Nielsen number in coincidence theory, J. Korean Math. Soc. 32 (1995), 171–181.
B. Jiang, Lectures on Nielsen Fixed Point Theory, vol. 14, American Mathematical Society, 1983.
B. Jiang, Fixed points and braids, Inv. Math. 75 (1984), 69–74.
B. Jiang, Fixed points and braids II, Math. Ann. 272 (1985), 249–256.
B. Jiang, A primer of Nielsen fixed point theory, Handbook of Topological Fixed Point Theory, Springer, Dordrecht, 2005, 617-647.
J. Jezierski, The least number of coincidence points on surfaces, J. Austral. Math. Soc. 58 (1995), 27–38.
J. Jezierski, The relative coincidence Nielsen number, Fund. Math. 149 (1996), 1–18.
M.R. Kelly, The relative Nielsen number and boundary-preserving surface maps, Pacific J. Math. 161 (1993), 139–153.
M.R. Kelly, Fixed points of boundary-preserving maps on punctured projective planes, Topology Appl. 124 (2002), 145–157.
M.R. Kelly, L.S. Silva and J.P. Vieria, Wecken property for coincidences of boundarypreserving maps between surfaces, Topology Appl. 293 (2021), paper no. 107556, 10 p.
T.-h. Kiang, The Theory of Fixed Point Classes, Springer–Verlag, Berlin, 1989.
H. Schirmer, A relative Nielsen number, Pacific J. Math. 122 (1986), 459–473.
F. Wecken, Fixpunktklassen III, Math. Ann. 118 (1942), 544–577.
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Prawa autorskie (c) 2023 Michael R. Kelly
Utwór dostępny jest na licencji Creative Commons Uznanie autorstwa – Bez utworów zależnych 4.0 Międzynarodowe.
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