The Nielsen Borsuk-Ulam number

被引：2

作者：

Cotrim, Fabiana Santos ^{[1
]}

Vendruscolo, Daniel ^{[2
]}

机构：

[1] Univ Fed Sao Carlos, Ctr Ciencias Nat, Buri, SP, Brazil

[2] Univ Fed Sao Carlos, Dept Matemat, Sao Carlos, SP, Brazil

来源：

BULLETIN OF THE BELGIAN MATHEMATICAL SOCIETY-SIMON STEVIN | 2017年 / 24卷 / 04期

基金：

巴西圣保罗研究基金会;

关键词：

Borsuk-Ulam Theorem; Nielsen theory; Coincidence theory; COINCIDENCE THEORY; MANIFOLDS;

D O I：

10.36045/bbms/1515035010

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

A Nielsen-Borsuk-Ulam number (NBU(f, tau)) is defined for continuous maps f : X -> Y where X and Y are closed orientable triangulable n-manifolds and X has a free involution tau. This number is a lower bound, in the homotopy class of f, for the number of pairs of points in X satisfying f (x) = f o tau(x). It is proved that NBU(f, tau) can be realized (Wecken type theorem) when n >= 3.

引用

页码：613 / 619

页数：7

共 8 条

[1] Nielsen coincidence theory applied to Borsuk-Ulam geometric problems [J].

Cotrim, Fabiana Santos ;

Vendruscolo, Daniel .

TOPOLOGY AND ITS APPLICATIONS, 2012, 159 (18) :3738-3745

[2] THE COINCIDENCE NIELSEN NUMBER ON NONORIENTABLE MANIFOLDS [J].

DOBRENKO, R ;

JEZIERSKI, J .

ROCKY MOUNTAIN JOURNAL OF MATHEMATICS, 1993, 23 (01) :67-85

[3] The Borsuk-Ulam theorem for homotopy spherical space forms [J].

Goncalves, Daciberg L. ;

Spreafico, Mauro ;

Neto, Oziride Manzoli .

JOURNAL OF FIXED POINT THEORY AND APPLICATIONS, 2011, 9 (02) :285-294

[4] The Borsuk-Ulam theorem for maps into a surface [J].

Goncalves, Daciberg Lima ;

Guaschi, John .

TOPOLOGY AND ITS APPLICATIONS, 2010, 157 (10-11) :1742-1759

[5]

Goncalves DL., 2006, Quaest. Math, V29, P117, DOI [10.2989/16073600609486153, DOI 10.2989/16073600609486153]

[6] THE SEMI-INDEX PRODUCT FORMULA [J].

JEZIERSKI, J .

FUNDAMENTA MATHEMATICAE, 1992, 140 (02) :99-120

[7] THE NIELSEN COINCIDENCE THEORY ON TOPOLOGICAL MANIFOLDS [J].

JEZIERSKI, J .

FUNDAMENTA MATHEMATICAE, 1993, 143 (02) :167-178

[8] Some generalizations of the Borsuk-Ulam Theorem [J].

Vendruscolo, Daniel ;

Desideri, Patricia E. ;

Pergher, Pedro L. Q. .

PUBLICATIONES MATHEMATICAE-DEBRECEN, 2011, 78 (3-4) :583-593

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