Geodesic
Nielsen theory of transversal fixed point sets (with an appendix: $C^∞$ and C0 fixed point sets are the same, by R. E. Greene)
Helga Schirmer1 ; Robert E. Greene2
1Department of Mathematics and Statistics Carleton University Ottawa, Canada K1S 5B6
2Department of Mathematics University of California 405 Hilgard Avenue Los Angeles, California 90024 U.S.A.
Fundamenta Mathematicae, Tome 141 (1992) no. 1, pp. 31-59
Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

Voir la notice de l'article

Examples exist of smooth maps on the boundary of a smooth manifold M which allow continuous extensions over M without fixed points but no such smooth extensions. Such maps are studied here in more detail. They have a minimal fixed point set when all transversally fixed maps in their homotopy class are considered. Therefore we introduce a Nielsen fixed point theory for transversally fixed maps on smooth manifolds without or with boundary, and use it to calculate the minimum number of fixed points in cases where continuous map extensions behave differently from smooth ones. In the appendix it is shown that a subset of a smooth manifold can be realized as the fixed point set of a smooth map in a given homotopy class if and only if it can be realized as the fixed point set of a continuous one. A special case of this result is used in a proof of the paper.
DOI : 10.4064/fm_1992_141_1_1_31_59
Keywords: transversally fixed maps, minimal and arbitrary fixed point sets, Nielsen fixed point theory, relative and extension Nielsen numbers

Helga Schirmer  1   ; Robert E. Greene  2

1 Department of Mathematics and Statistics Carleton University Ottawa, Canada K1S 5B6
2 Department of Mathematics University of California 405 Hilgard Avenue Los Angeles, California 90024 U.S.A. 
@article{10_4064_fm_1992_141_1_1_31_59,
     author = {Helga Schirmer and Robert E. Greene},
     title = {Nielsen theory of transversal fixed point sets (with an appendix: $C^\ensuremath{\infty}$ and {C0} fixed point sets are the same, by {R.} {E.} {Greene)}},
     journal = {Fundamenta Mathematicae},
     pages = {31--59},
     year = {1992},
     volume = {141},
     number = {1},
     doi = {10.4064/fm_1992_141_1_1_31_59},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.4064/fm_1992_141_1_1_31_59/}
}
TY  - JOUR
AU  - Helga Schirmer
AU  - Robert E. Greene
TI  - Nielsen theory of transversal fixed point sets (with an appendix: $C^∞$ and C0 fixed point sets are the same, by R. E. Greene)
JO  - Fundamenta Mathematicae
PY  - 1992
SP  - 31
EP  - 59
VL  - 141
IS  - 1
UR  - http://geodesic.mathdoc.fr/articles/10.4064/fm_1992_141_1_1_31_59/
DO  - 10.4064/fm_1992_141_1_1_31_59
LA  - en
ID  - 10_4064_fm_1992_141_1_1_31_59
ER  - 
%0 Journal Article
%A Helga Schirmer
%A Robert E. Greene
%T Nielsen theory of transversal fixed point sets (with an appendix: $C^∞$ and C0 fixed point sets are the same, by R. E. Greene)
%J Fundamenta Mathematicae
%D 1992
%P 31-59
%V 141
%N 1
%U http://geodesic.mathdoc.fr/articles/10.4064/fm_1992_141_1_1_31_59/
%R 10.4064/fm_1992_141_1_1_31_59
%G en
%F 10_4064_fm_1992_141_1_1_31_59
Helga Schirmer; Robert E. Greene. Nielsen theory of transversal fixed point sets (with an appendix: $C^∞$ and C0 fixed point sets are the same, by R. E. Greene). Fundamenta Mathematicae, Tome 141 (1992) no. 1, pp. 31-59. doi: 10.4064/fm_1992_141_1_1_31_59

Cité par Sources :