Geodesic
Minimal $m$-handle decomposition of three-dimensional handlebodies
Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, no. 2 (2013), pp. 106-110 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

For the $3$-dimensional handlebody we build an $m$-handle decomposition with minimal number of handles and prove a criterion of minimality. It is proved that two functions can be connected by a path in the $m$-function space without inner critical points on the solid torus if they have the same number of critical points of each index. 
@article{BASM_2013_2_a11,
     author = {Alexander Prishlyak and Elena Vyatchaninova},
     title = {Minimal $m$-handle decomposition of three-dimensional handlebodies},
     journal = {Buletinul Academiei de \c{S}tiin\c{t}e a Republicii Moldova. Matematica},
     pages = {106--110},
     year = {2013},
     number = {2},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/BASM_2013_2_a11/}
}
TY  - JOUR
AU  - Alexander Prishlyak
AU  - Elena Vyatchaninova
TI  - Minimal $m$-handle decomposition of three-dimensional handlebodies
JO  - Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica
PY  - 2013
SP  - 106
EP  - 110
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/BASM_2013_2_a11/
LA  - en
ID  - BASM_2013_2_a11
ER  - 
%0 Journal Article
%A Alexander Prishlyak
%A Elena Vyatchaninova
%T Minimal $m$-handle decomposition of three-dimensional handlebodies
%J Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica
%D 2013
%P 106-110
%N 2
%U http://geodesic.mathdoc.fr/item/BASM_2013_2_a11/
%G en
%F BASM_2013_2_a11
Alexander Prishlyak; Elena Vyatchaninova. Minimal $m$-handle decomposition of three-dimensional handlebodies. Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, no. 2 (2013), pp. 106-110. http://geodesic.mathdoc.fr/item/BASM_2013_2_a11/

[1] Sharko V., “Functions on the surfaces, I”, Some contemporary problems in mathematics, Proc. In-t of Math. NASU, 25, Kiev, 1998, 408–434 | MR

[2] Maksymenko S. I., “Path-components of Morse mappings spaces of surface”, Comment. Math. Helv., 80 (2005), 655–690 | DOI | MR | Zbl

[3] Hajduk B., “Minimal $m$-functions”, Fund. math., 110 (1981), 178–200 | MR

[4] Jankowski A., Rubinsztein R., “Functions with non-degenerated critical points on manifolds with boundary”, Comm. Math., 16 (1972), 99–112 | MR | Zbl

[5] Prishlyak O. O., Prishlyak K. O., Vyatchaninova O. N., “Homotopic classification of noncritical $m$-functions on 3-disk”, J. Num. Appl. Math., 110 (2012), 113–119