Geodesic
Relations amongst twists along Montesinos twins in the 4-sphere
Gay, David T1 ; Hartman, Daniel1
1Department of Mathematics, University of Georgia, Athens, GA, United States
Algebraic and Geometric Topology, Tome 25 (2025) no. 1, pp. 287-299
Cet article a éte moissonné depuis la source Mathematical Sciences Publishers

Voir la notice de l'article

Isotopy classes of diffeomorphisms of the 4-sphere can be described either from a Cerf-theoretic perspective in terms of loops of 5-dimensional handle attaching data, starting and ending with handles in canceling position, or via certain twists along submanifolds analogous to Dehn twists in dimension 2. The subgroup of the smooth mapping class group of the 4-sphere coming from loops of 5-dimensional handles of index 1 and 2 coincides with the subgroup generated by twists along Montesinos twins (pairs of 2-spheres intersecting transversely twice) in which one of the two 2-spheres in the twin is unknotted. We show that this subgroup is in fact trivial or cyclic of order 2.

DOI : 10.2140/agt.2025.25.287
Keywords: pseudoisotopy, Montesinos twins, diffeomorphism, isotopy, 4-manifold, mapping class group

Gay, David T  1   ; Hartman, Daniel  1

1 Department of Mathematics, University of Georgia, Athens, GA, United States 
@article{10_2140_agt_2025_25_287,
     author = {Gay, David T and Hartman, Daniel},
     title = {Relations amongst twists along {Montesinos} twins in the 4-sphere},
     journal = {Algebraic and Geometric Topology},
     pages = {287--299},
     year = {2025},
     volume = {25},
     number = {1},
     doi = {10.2140/agt.2025.25.287},
     url = {http://geodesic.mathdoc.fr/articles/10.2140/agt.2025.25.287/}
}
TY  - JOUR
AU  - Gay, David T
AU  - Hartman, Daniel
TI  - Relations amongst twists along Montesinos twins in the 4-sphere
JO  - Algebraic and Geometric Topology
PY  - 2025
SP  - 287
EP  - 299
VL  - 25
IS  - 1
UR  - http://geodesic.mathdoc.fr/articles/10.2140/agt.2025.25.287/
DO  - 10.2140/agt.2025.25.287
ID  - 10_2140_agt_2025_25_287
ER  - 
%0 Journal Article
%A Gay, David T
%A Hartman, Daniel
%T Relations amongst twists along Montesinos twins in the 4-sphere
%J Algebraic and Geometric Topology
%D 2025
%P 287-299
%V 25
%N 1
%U http://geodesic.mathdoc.fr/articles/10.2140/agt.2025.25.287/
%R 10.2140/agt.2025.25.287
%F 10_2140_agt_2025_25_287
Gay, David T; Hartman, Daniel. Relations amongst twists along Montesinos twins in the 4-sphere. Algebraic and Geometric Topology, Tome 25 (2025) no. 1, pp. 287-299. doi: 10.2140/agt.2025.25.287

[1] R Budney, D Gabai, Knotted 3-balls in S4, preprint (2019)

[2] J Cerf, La stratification naturelle des espaces de fonctions différentiables réelles et le théorème de la pseudo-isotopie, Inst. Hautes Études Sci. Publ. Math. 39 (1970) 5

[3] D T Gay, Diffeomorphisms of the 4-sphere, Cerf theory and Montesinos twins, preprint (2021)

[4] M Golubitsky, V Guillemin, Stable mappings and their singularities, 14, Springer (1973) | DOI

[5] J M Montesinos, On twins in the four-sphere, I, Quart. J. Math. Oxford Ser. 34 (1983) 171 | DOI

[6] J M Montesinos, On twins in the four-sphere, II, Quart. J. Math. Oxford Ser. 35 (1984) 73 | DOI

[7] C T C Wall, Diffeomorphisms of 4-manifolds, J. London Math. Soc. 39 (1964) 131 | DOI

Cité par Sources :