Author(s): Vieira, J. P. [UNESP] ; Silva, L. S.
Date: 2020
Persistent ID: http://hdl.handle.net/11449/201115
Origin: Oasisbr
Subject(s): Coincidence; fibre-preserving maps; T-fibre bundles; Coincidence; Coincidence; fibre-preserving maps; fibre-preserving maps; T-fibre bundles; T-fibre bundles
Made available in DSpace on 2020-12-12T02:24:28Z (GMT). No. of bitstreams: 0 Previous issue date: 2020-06-01
Let f, g: M(ϕ1) → M(ϕ2) be fibre-preserving maps over the circle, S1, where M(ϕ1) and M(ϕ2) are fibre bundles over S1 and the fibre is the torus, T. The main purpose of this work is to classify the pairs of maps (f, g) which can be deformed by fibrewise homotopy over S1 to a coincidence-free pair (f′, g′) , f′, g′: M(ϕ1) → M(ϕ2). In general, the classification of such pairs of maps is equivalent to finding solutions for an equation in the free group π2(T, T- 1) , called the main equation. In certain situations, it is appropriate to study the main equation in the abelianization of π2(T, T- 1) or on some quotients of this group, since, if the equation in one of these quotients does not admit solution, then the original equation also does not admit solution. In this case, it is not possible to obtain the desired deformability.
Instituto de Geociências e Ciências Exatas Universidade Estadual Paulista (UNESP)
Campus Avançado Tupã Instituto Federal de Educação Ciência e Tecnologia de São Paulo (IFSP)
Instituto de Geociências e Ciências Exatas Universidade Estadual Paulista (UNESP)
