The degree of a map between surfaces

1987 ◽  
Vol 276 (3) ◽  
pp. 415-423 ◽  
Author(s):  
Richard Skora
Keyword(s):  
Degree Of A Map

Isometric folding of Riemannian manifolds

1978 ◽  
Vol 79 (3-4) ◽  
pp. 275-284 ◽  
Author(s):  
S. A. Robertson
Keyword(s):  
Riemannian Manifolds ◽  
Main Technique ◽  
Degree Of A Map ◽  
Simple Rules

SynopsisWhen a sheet of paper is crumpled in the hands and then crushed flat against a desk-top, the pattern of creases so formed is governed by certain simple rules. These rules generalize to theorems on folding Riemannian manifolds isometrically into one another. The most interesting results apply to the case in which domain and codomain have the same dimension. The main technique of proof combines the notion of volume with Hopf's concept of the degree of a map.

scholarly journals LINKING NUMBER IN A PROJECTIVE SPACE AS THE DEGREE OF A MAP

2007 ◽  
Vol 16 (04) ◽  
pp. 489-497 ◽  
Author(s):  
JULIA VIRO DROBOTUKHINA
Keyword(s):  
Projective Space ◽  
Configuration Space ◽  
The Self ◽  
Real Projective Space ◽  
3 Dimensional ◽  
Linking Number ◽  
Degree Of A Map ◽  
Number Of Cycles ◽  
Dimensional Projective Space

For any two disjoint oriented circles embedded into the 3-dimensional real projective space, we construct a 3-dimensional configuration space and its map to the projective space such that the linking number of the circles is the half of the degree of the map. Similar interpretations are given for the linking number of cycles in a projective space of arbitrary odd dimension and the self-linking number of a zero homologous knot in the 3-dimensional projective space.

Theory of Index for Dynamical Systems of Order Higher Than Two

1980 ◽  
Vol 47 (2) ◽  
pp. 421-427 ◽  
Author(s):  
C. S. Hsu
Keyword(s):  
Vector Field ◽  
Dynamical Systems ◽  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Higher Order ◽  
Abstract Concept ◽  
Basic Tool ◽  
Degree Of A Map

This paper is concerned with the generalization of Poincare´’s theory of index to systems of order higher than two. The basic tool used in the generalization is the concept of the degree of a map. In topology this concept has been used to discuss the index of a vector field. In this paper we shall use the degree of a map concept to present a theory of index for higher-order systems in a form which might make it more accessible to engineers for applications. The theory utilizes the notion of the index of a hypersurface with respect to a given vector field. After presenting the theory, it is applied to dynamical systems governed by ordinary differential equations and also to dynamical systems governed by point mappings. Finally, in order to show how the abstract concept of the degree of a map, hence the index of a surface, may actually be evaluated, illustrative procedures of evaluation for two kinds of hypersurfaces are discussed in detail and an example of application is given.

The Degree of a Map

1966 ◽  
Vol s3-16 (1) ◽  
pp. 369-383 ◽  
Author(s):  
D. B. A. Epstein
Keyword(s):  
Degree Of A Map

scholarly journals On the Integral Giving the Degree of a Map and a Rouché Type Theorem

1997 ◽  
Vol 16 (2) ◽  
pp. 239-247 ◽  
Author(s):  
T. Hatziafratis ◽  
A. Tsarpalias
Keyword(s):  
Type Theorem ◽  
Degree Of A Map
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