In his work, was applied crossings between pairs of variables, homogeneity test and technical exhaustive AID （Automatic Interaction Detection） for formation of groups second sample each of the following deficiencies...In his work, was applied crossings between pairs of variables, homogeneity test and technical exhaustive AID （Automatic Interaction Detection） for formation of groups second sample each of the following deficiencies： see, listen, move and intellectual from database obtained from the 2010 Population Census data sample （respondents Complete Questionnaire） formed by 20,635,472 people interviewed all over the country with the objective of studying relationship between different variables such as disability, level of education, gender, income in minimum wages among others.展开更多
Let X be a topological space.In this survey the authors consider several types of configuration spaces,namely,the classical(usual)configuration spaces F_n(X)and D_n(X),the orbit configuration spaces F_n^G(X)and F_n^G(...Let X be a topological space.In this survey the authors consider several types of configuration spaces,namely,the classical(usual)configuration spaces F_n(X)and D_n(X),the orbit configuration spaces F_n^G(X)and F_n^G(X)/S_nwith respect to a free action of a group G on X,and the graph configuration spaces F_n~Γ(X)and F_n~Γ(X)/H,whereΓis a graph and H is a suitable subgroup of the symmetric group S_n.The ordered configuration spaces F_n(X),F_n^G(X),F_n~Γ(X)are all subsets of the n-fold Cartesian product ∏_1~nX of X with itself,and satisfy F_n^G(X)?F_n(X)?F_n~Γ(X)?∏_1~nX.If A denotes one of these configuration spaces,the authors analyse the difference between A and ∏_1~nXfrom a topological and homotopical point of view.The principal results known in the literature concern the usual configuration spaces.The authors are particularly interested in the homomorphism on the level of the homotopy groups of the spaces induced by the inclusionι:A-→∏_1~nX,the homotopy type of the homotopy fibre I_ιof the mapιvia certain constructions on various spaces that depend on X,and the long exact sequence in homotopy of the fibration involving I_ιand arising from the inclusionι.In this respect,if X is either a surface without boundary,in particular if X is the 2-sphere or the real projective plane,or a space whose universal covering is contractible,or an orbit space S^k/Gof the k-dimensional sphere by a free action of a Lie group G,the authors present recent results obtained by themselves for the first case,and in collaboration with Golasi′nski for the second and third cases.The authors also briefly indicate some older results relative to the homotopy of these spaces that are related to the problems of interest.In order to motivate various questions,for the remaining types of configuration spaces,a few of their basic properties are described and proved.A list of open questions and problems is given at the end of the paper.展开更多
文摘In his work, was applied crossings between pairs of variables, homogeneity test and technical exhaustive AID （Automatic Interaction Detection） for formation of groups second sample each of the following deficiencies： see, listen, move and intellectual from database obtained from the 2010 Population Census data sample （respondents Complete Questionnaire） formed by 20,635,472 people interviewed all over the country with the objective of studying relationship between different variables such as disability, level of education, gender, income in minimum wages among others.
基金supported by the CNRS/FAPESP programme no226555(France)and n^(o) 2014/50131-7(Brazil)FAPESP–Fundacao de Amparo a Pesquisa do Estado de Sao Paulo,Projeto Tematico Topologia Algebrica,Geometrica 2012/24454-8(Brazil)for partial supportthe Institute for Mathematical Sciences,National University of Singapore
文摘Let X be a topological space.In this survey the authors consider several types of configuration spaces,namely,the classical(usual)configuration spaces F_n(X)and D_n(X),the orbit configuration spaces F_n^G(X)and F_n^G(X)/S_nwith respect to a free action of a group G on X,and the graph configuration spaces F_n~Γ(X)and F_n~Γ(X)/H,whereΓis a graph and H is a suitable subgroup of the symmetric group S_n.The ordered configuration spaces F_n(X),F_n^G(X),F_n~Γ(X)are all subsets of the n-fold Cartesian product ∏_1~nX of X with itself,and satisfy F_n^G(X)?F_n(X)?F_n~Γ(X)?∏_1~nX.If A denotes one of these configuration spaces,the authors analyse the difference between A and ∏_1~nXfrom a topological and homotopical point of view.The principal results known in the literature concern the usual configuration spaces.The authors are particularly interested in the homomorphism on the level of the homotopy groups of the spaces induced by the inclusionι:A-→∏_1~nX,the homotopy type of the homotopy fibre I_ιof the mapιvia certain constructions on various spaces that depend on X,and the long exact sequence in homotopy of the fibration involving I_ιand arising from the inclusionι.In this respect,if X is either a surface without boundary,in particular if X is the 2-sphere or the real projective plane,or a space whose universal covering is contractible,or an orbit space S^k/Gof the k-dimensional sphere by a free action of a Lie group G,the authors present recent results obtained by themselves for the first case,and in collaboration with Golasi′nski for the second and third cases.The authors also briefly indicate some older results relative to the homotopy of these spaces that are related to the problems of interest.In order to motivate various questions,for the remaining types of configuration spaces,a few of their basic properties are described and proved.A list of open questions and problems is given at the end of the paper.
