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THE HOMOTOPY TYPE OF THE SPACE OF GRADIENT VECTOR FIELDS ON THE TWO-DIMENSIONAL DISC

Published online by Cambridge University Press:  30 March 2012

PIOTR BARTŁOMIEJCZYK  and
PIOTR NOWAK-PRZYGODZKI
PIOTR BARTŁOMIEJCZYK
Affiliation:
Institute of Mathematics, University of Gdańsk, Wita Stwosza 57, 80-952 Gdańsk, Poland e-mail: pb@mat.ug.edu.pl, web page: http://pb.mat.ug.edu.pl
PIOTR NOWAK-PRZYGODZKI
Affiliation:
Faculty of Applied Physics and Mathematics, Gdańsk University of Technology, Gabriela Narutowicza 11/12, 80-233 Gdańsk, Poland e-mail: piotrnp@wp.pl
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Abstract

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We prove that the inclusion of the space of gradient vector fields into the space of all vector fields on D2 non-vanishing in S1 is a homotopy equivalence.

Keywords

Primary: 55Q05Secondary: 37B35
Type
Research Article
Information
Glasgow Mathematical Journal , Volume 54 , Issue 3 , September 2012 , pp. 619 - 626
Copyright
Copyright © Glasgow Mathematical Journal Trust 2012

References

REFERENCES

1.Balanov, Z., Krawcewicz, W., Rybicki, S. and Steinlein, H., A short treatise on the equivariant degree theory and its applications, J. Fixed Point Theory Appl. 8 (2010), 1–74.CrossRefGoogle Scholar
2.Balanov, Z., Krawcewicz, W. and Steinlein, H., in Applied Equivariant Degree, (American Institute for Mathematical Sciences, Springfield, MO, 2006).Google Scholar
3.Bartłomiejczyk, P., Gȩba, K. and Izydorek, M., Otopy classes of equivariant local maps, J. Fixed Point Theory Appl. 25 (2010), 195–203.Google Scholar
4.Dancer, E. N., Gȩba, K. and Rybicki, S., Classification of homotopy classes of gradient equivariant maps, Fund. Math. 185 (2005), 1–18.CrossRefGoogle Scholar
5.Parusiński, A., Gradient homotopies of gradient vector fields, Studia Math. XCVI (1990), 73–80.CrossRefGoogle Scholar