Some generalizations of the Borsuk–Ulam theorem and applications to realizing homotopy classes by embedded spheres-Reference-Cited by-同舟云学术

Some generalizations of the Borsuk–Ulam theorem and applications to realizing homotopy classes by embedded spheres

Published:1973-09 Issue:2 Volume:74 Page:251-256
ISSN:0305-0041
Container-title:Mathematical Proceedings of the Cambridge Philosophical Society
language:en
Short-container-title:Math. Proc. Camb. Phil. Soc.

Author:

Fenn Roger

Abstract

In this paper, some theorems of the Borsuk-Ulam type (1) are given. One of these can be applied to show that certain homotopy classes in manifolds cannot be realized by embedded spheres. The n-dimensional sphere Sn is the subset of the euclidean spaceRn+l consisting of all points (x1, …,xn+1) satisfying . Let be a piecewise linear (PL) involution on Sn without fixed points.

Publisher

Cambridge University Press (CUP)

Subject

General Mathematics

Reference8 articles.

1. Surgery on Compact Manifolds

2. Drei Sätze über die n-dimensionale euklidische Sphäre

3. ON 2-SPHERES IN 4-MANIFOLDS

4. Geometric and algebraic intersection numbers

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