Closed Coverings in Cech Homology Theory

1957 ◽  
Vol 84 (2) ◽  
pp. 319
Author(s):  
E. E. Floyd









1970 ◽  
Vol 21 (2) ◽  
pp. 229-237 ◽  
Author(s):  
S. K. Kaul


Author(s):  
S. Buonchristiano ◽  
C. P. Rourke ◽  
B. J. Sanderson


2010 ◽  
Vol 17 (2) ◽  
pp. 391-404
Author(s):  
Mikael Vejdemo-Johansson

Abstract Kadeishvili's proof of theminimality theorem [T. Kadeishvili, On the homology theory of fiber spaces, Russ. Math. Surv. 35:3 (1980), 231–238] induces an algorithm for the inductive computation of an A ∞-algebra structure on the homology of a dg-algebra. In this paper, we prove that for one class of dg-algebras, the resulting computation will generate a complete A ∞-algebra structure after a finite amount of computational work.



2021 ◽  
Vol 19 (1) ◽  
pp. 706-723
Author(s):  
Yuri V. Muranov ◽  
Anna Szczepkowska

Abstract In this paper, we introduce the category and the homotopy category of edge-colored digraphs and construct the functorial homology theory on the foundation of the path homology theory provided by Grigoryan, Muranov, and Shing-Tung Yau. We give the construction of the path homology theory for edge-colored graphs that follows immediately from the consideration of natural functor from the category of graphs to the subcategory of symmetrical digraphs. We describe the natural filtration of path homology groups of any digraph equipped with edge coloring, provide the definition of the corresponding spectral sequence, and obtain commutative diagrams and braids of exact sequences.



1956 ◽  
Vol 63 (2) ◽  
pp. 248 ◽  
Author(s):  
Andrew H. Wallace


1942 ◽  
Vol 43 (2) ◽  
pp. 370 ◽  
Author(s):  
W. Mayer
Keyword(s):  


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