PARAMETRISED TOPOLOGICAL COMPLEXITY OF GROUP EPIMORPHISMS

被引：3

作者：

Grant, Mark ^{[1
]}

机构：

[1] Univ Aberdeen, Inst Math, Fraser Noble Bldg, Aberdeen AB24 3UE, Scotland

来源：

TOPOLOGICAL METHODS IN NONLINEAR ANALYSIS | 2022年 / 60卷 / 01期

关键词：

Parametrised topological complexity; aspherical space; group epimorphisms; MOTION; CATEGORY;

D O I：

10.12775/TMNA.2021.056

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We show that the parametrised topological complexity of Cohen, Farber and Weinberger gives an invariant of group epimorphisms. We extend various bounds for the topological complexity of groups to obtain bounds for the parametrised topological complexity of epimorphisms. Several applications are given, including an alternative computation of the parametrised topological complexity of the planar Fadell-Neuwirth fibrations which avoids calculations involving cup products. We also prove a homotopy invariance result for parametrised topological complexity of fibrations over different bases.

引用

页码：287 / 303

页数：17

共 21 条

[1] The sectional category of a map [J].

Arkowitz, M ;

Strom, J .

PROCEEDINGS OF THE ROYAL SOCIETY OF EDINBURGH SECTION A-MATHEMATICS, 2004, 134 :639-652

[2] GROUPS WITH HOMOLOGICAL DUALITY GENERALIZING POINCARE DUALITY [J].

BIERI, R ;

ECKMANN, B .

INVENTIONES MATHEMATICAE, 1973, 20 (02) :103-124

[3] On the sectional category of subgroup inclusions and Adamson cohomology theory [J].

Blaszczyk, Zbigniew ;

Carrasquel-Vera, Jose Gabriel ;

Baro, Arturo Espinosa .

JOURNAL OF PURE AND APPLIED ALGEBRA, 2022, 226 (06)

[4]

Cohen D.C., 2021, J. Topol. Anal., DOI [10.1142/S1793525321500631, DOI 10.1142/S1793525321500631]

[5] Topology of Parametrized Motion Planning Algorithms [J].

Cohen, Daniel C. ;

Farber, Michael ;

Weinberger, Shmuel .

SIAM JOURNAL ON APPLIED ALGEBRA AND GEOMETRY, 2021, 5 (02) :229-249

[6] Homology of iterated semidirect products of free groups [J].

Cohen, DC ;

Suciu, AI .

JOURNAL OF PURE AND APPLIED ALGEBRA, 1998, 126 (1-3) :87-120

[7] ON TOPOLOGICAL COMPLEXITY OF HYPERBOLIC GROUPS [J].

Dranishnikov, Alexander .

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 2020, 148 (10) :4547-4556

[8] ON THE LUSTERNIK-SCHNIRELMANN CATEGORY OF ABSTRACT GROUPS [J].

EILENBERG, S ;

GANEA, T .

ANNALS OF MATHEMATICS, 1957, 65 (03) :517-518

[9]

Fadell Edward., 1962, MATH SCAND, V10, P111, DOI DOI 10.7146/MATH.SCAND.A-10517

[10]

Farber M, 2006, NATO SCI SER II-MATH, V217, P185

← 1 2 3 →