scholarly journals Extended graph rotation systems as a model for cyclic weaving on orientable surfaces

2015 ◽  
Vol 193 ◽  
pp. 61-79 ◽  
Author(s):  
Ergun Akleman ◽  
Jianer Chen ◽  
Jonathan L. Gross
Keyword(s):  
Extended Graph ◽  
Orientable Surfaces

scholarly journals Invariants of Stable Maps between Closed Orientable Surfaces

Mathematics ◽  
2021 ◽  
Vol 9 (3) ◽  
pp. 215
Author(s):  
Catarina Mendes de Jesus S. ◽  
Pantaleón D. Romero
Keyword(s):  
Point Of View ◽  
Stable Maps ◽  
Smooth Maps ◽  
Orientable Surfaces

In this paper, we will consider the problem of constructing stable maps between two closed orientable surfaces M and N with a given branch set of curves immersed on N. We will study, from a global point of view, the behavior of its families in different isotopies classes on the space of smooth maps. The main goal is to obtain different relationships between invariants. We will provide a new proof of Quine’s Theorem.

A Polynomial Invariant of Graphs On Orientable Surfaces

2001 ◽  
Vol 83 (3) ◽  
pp. 513-531 ◽  
Author(s):  
Béla Bollobás ◽  
Oliver Riordan
Keyword(s):  
Polynomial Invariant ◽  
Orientable Surfaces

Stable bi-maps from closed orientable surfaces to R x R

2021 ◽  
Author(s):  
Catarina Mendes de Jesus ◽  
Erica Boizan Batista ◽  
João Carlos Ferreira Costa
Keyword(s):  
Orientable Surfaces
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