Geodesic
Minimal $m$-handle decomposition of three-dimensional handlebodies
Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, no. 2 (2013), pp. 106-110

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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. 
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     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},
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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/