### Removing isolated zeroes by homotopy

DOI: http://dx.doi.org/10.12775/TMNA.2019.042

#### Abstract

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#### References

H. Aikawa, Hölder continuity of the Dirichlet solution for a general domain, Bull. London Math. Soc. 34 (2002), no. 6, 691–702.

D. Anker, On Removing Isolated Zeroes of Vector Fields by Perturbation, Ph.D. Thesis, University of Michigan, 1981.

D. Anker, On removing isolated zeroes of vector fields by perturbation, Nonlinear Anal. 8 (1984), no. 9, 1005–1112.

P. Baum, Quadratic maps and stable homotopy groups of spheres, Illinois J. Math. 11 (1967), 586–595.

J. Bochnak, M. Coste and M. Roy, Real Algebraic Geometry, MSM, vol. 36, Springer, 1998.

R. Brown, M. Furi, L. Górniewicz and B. Jiang (eds.), Handbook of Topological Fixed Point Theory, Springer, 2005.

A. Coffman, CR singular immersions of complex projective spaces, Beiträge zur Algebra und Geometrie 43 (2002), no. 2, 451–477.

A. Coffman, Real congruence of complex matrix pencils and complex projections of real Veronese varieties, Linear Algebra Appl. 370 (2003), 41–83.

E.N. Dancer, On the existence of zeros of perturbed operators, Nonlinear Anal. 7 (1983), no. 7, 717–727.

E.N. Dancer, Bifurcation under continuous groups of symmetries, Systems of Nonlinear Partial Differential Equations (Oxford, 1982), 343–350; NATO ASI Ser. C 111, Reidel, Dordrecht, 1983.

E.N. Dancer, Perturbation of zeros in the presence of symmetries, J. Austral. Math. Soc. Ser. A 36 (1984), no. 1, 106–125.

F. Deloup, The fundamental group of the circle is trivial, Amer. Math. Monthly 112 (2005), no. 5, 417–425.

A. Elgindi, A topological obstruction to the removal of a degenerate complex tangent and some related homotopy and homology groups, Internat. J. Math. 26 (2015), no. 5, 1550025, 16 pp.

M. Fenille, Epsilon Nielsen coincidence theory, Cent. Eur. J. Math. 12 (2014), no. 9, 1337–1348.

P. Garabedian, Partial Differential Equations, Wiley, 1964.

D. Gilbarg and N. Trudinger, Elliptic Partial Differential Equations of Second Order, Springer, CIM, 2001.

O.A. Ladyzhenskaya and N.N. Ural’tseva, Linear and Quasilinear Elliptic Equations, 1964 (in Russian); English transl.: Academic Press, 1968.

J. Lee, Introduction to Smooth Manifolds, second ed., GTM, vol. 218, Springer, 2013.

V.G. Maz’ya, Notes on Hölder regularity of a boundary point with respect to an elliptic operator of second order, Problemy Matematicheskogo Analiza 74 (2013), 117–121; English transl.: J. Math. Sci. (N.Y.) 196 (2014), no. 4, 572–577.

M. Nestler, I. Nitschke, S. Praetorius and A. Voigt, Orientational order on surfaces: the coupling of topology, geometry, and dynamics, J. Nonlinear Sci. 28 (2018), no. 1, 147–191.

J. Palis and C. Pugh, Fifty problems in dynamical systems, Dynamical Systems, Warwick 1974, 345–353; LNM 468, Springer, 1975.

C. Simon and C. Titus, Removing index-zero singularities with C1 -small perturbations, Dynamical Systems, Warwick 1974, 278–286; LNM 468, Springer, 1975.

E. Spanier, Algebraic Topology, McGraw-Hill, 1966.

R. Wood, Polynomial maps from spheres to spheres, Invent. Math. 5 (1968), 163–168.

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