Geodesic
Strong topological rigidity of noncompact orientable surfaces
Das, Sumanta1
1 Department of Mathematics, Indian Institute of Science, Bangalore, India
Algebraic and Geometric Topology, Tome 24 (2024) no. 8, pp. 4423-4469

Voir la notice de l'article provenant de la source Mathematical Sciences Publishers

We show that every orientable infinite-type surface is properly rigid as a consequence of a more general result. Namely, we prove that if a homotopy equivalence between any two noncompact orientable surfaces is a proper map, then it is properly homotopic to a homeomorphism, provided the surfaces are neither the plane nor the punctured plane. Thus all noncompact orientable surfaces, except the plane and the punctured plane, are topologically rigid in a strong sense.

DOI : 10.2140/agt.2024.24.4423
Keywords: topological rigidity, infinite-type surfaces, Dehn–Nielsen–Baer theorem

Das, Sumanta 1

1 Department of Mathematics, Indian Institute of Science, Bangalore, India 
@article{10_2140_agt_2024_24_4423,
     author = {Das, Sumanta},
     title = {Strong topological rigidity of noncompact orientable surfaces},
     journal = {Algebraic and Geometric Topology},
     pages = {4423--4469},
     publisher = {mathdoc},
     volume = {24},
     number = {8},
     year = {2024},
     doi = {10.2140/agt.2024.24.4423},
     url = {http://geodesic.mathdoc.fr/articles/10.2140/agt.2024.24.4423/}
}
TY  - JOUR
AU  - Das, Sumanta
TI  - Strong topological rigidity of noncompact orientable surfaces
JO  - Algebraic and Geometric Topology
PY  - 2024
SP  - 4423
EP  - 4469
VL  - 24
IS  - 8
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.2140/agt.2024.24.4423/
DO  - 10.2140/agt.2024.24.4423
ID  - 10_2140_agt_2024_24_4423
ER  - 
%0 Journal Article
%A Das, Sumanta
%T Strong topological rigidity of noncompact orientable surfaces
%J Algebraic and Geometric Topology
%D 2024
%P 4423-4469
%V 24
%N 8
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.2140/agt.2024.24.4423/
%R 10.2140/agt.2024.24.4423
%F 10_2140_agt_2024_24_4423
Das, Sumanta. Strong topological rigidity of noncompact orientable surfaces. Algebraic and Geometric Topology, Tome 24 (2024) no. 8, pp. 4423-4469. doi: 10.2140/agt.2024.24.4423

Cité par Sources :