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| Weak Graph Map Homotopy and Its Applications∗ |
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Citation： |
Conglei ZHANG,Yanying WANG,Zhiguo ZHANG,Yan ZHAO.Weak Graph Map Homotopy and Its Applications∗[J].Chinese Annals of Mathematics B,2024,45(2):235~252 |
| Page view： 1071
Net amount： 503 |
Authors： |
Conglei ZHANG; Yanying WANG;Zhiguo ZHANG;Yan ZHAO |
Foundation： |
This work was supported by the National Natural Science Foundation of China (No. 11771116). |
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| Abstract： |
The authors introduce a notion of a weak graph map homotopy (they call it
M-homotopy), discuss its properties and applications. They prove that the weak graph
map homotopy equivalence between graphs coincides with the graph homotopy equivalence
defined by Yau et al in 2001. The difference between them is that the weak graph map
homotopy transformation is defined in terms of maps, while the graph homotopy transformation is defined by means of combinatorial operations. They discuss its advantages over
the graph homotopy transformation. As its applications, they investigate the mapping
class group of a graph and the 1-order MP-homotopy group of a pointed simple graph.
Moreover, they show that the 1-order MP-homotopy group of a pointed simple graph is
invariant up to the weak graph map homotopy equivalence. |
Keywords： |
Weak graph map homotopy, Trivial vertex, Strong deformation retract,
Mapping class group, MP-Homotopy group |
Classification： |
55P10, 55Q70, 05C99, 05C38 |
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