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2019 ◽  
Vol 26 (2) ◽  
pp. 303-309
Author(s):  
Samson Saneblidze

Abstract Let {Y=\lvert X\rvert} be the geometric realization of a path-connected simplicial set X, and let {G=\pi_{1}(X)} be the fundamental group. Given a subgroup {H\subset G} , let {G/H} be the set of cosets. Using the combinatorial model {\boldsymbol{\Omega}X\to\mathbf{P}X\to X} of the path fibration {{\Omega}Y\to{P}Y\to Y} and a canonical action {\mu\colon\boldsymbol{\Omega}X\times G/H\to G/H} , we construct a covering map {G/H\to Y_{H}\to Y} as the geometric realization of the associated short sequence {G/H\to\mathbf{P}X\times_{\mu}G/H\to X} . This construction, in particular, does not use the existence of a maximal tree in X. For a 2-dimensional X and {H=\{1\}} , it can also be viewed as a simplicial approximation of a Cayley 2-complex of G.



2014 ◽  
Vol 89 (6) ◽  
Author(s):  
Huy Nguyen Le ◽  
Yu Cai ◽  
Xingyao Wu ◽  
Rafael Rabelo ◽  
Valerio Scarani
Keyword(s):  


2006 ◽  
Vol 20 (30n31) ◽  
pp. 4992-5007
Author(s):  
RAYMOND F. BISHOP ◽  
NORBERT LIGTERINK ◽  
NIELS R. WALET

A consistent approach to Hamiltonian SU (N) lattice gauge field theory is developed using the maximal-tree gauge and an appropriately chosen set of angular variables. The various constraints are carefully discussed, as is a practical means for their implementation. A complete set of variables for the colourless sector is thereby determined. We show that the one-plaquette problem in SU (N) gauge theory can be mapped onto a problem of N fermions on a torus, which is solved numerically for the low-lying energy spectra for N ≤ 5. We end with a brief discussion of how to extend the approach to include the spatial (inter-plaquette) correlations of the full theory, by using a coupled-cluster method parametrisation of the full wave functional.



2006 ◽  
Vol 11 (2) ◽  
pp. 219-229 ◽  
Author(s):  
Xujin Chen ◽  
Xiaodong Hu ◽  
Tianping Shuai
Keyword(s):  


1991 ◽  
Vol 40 (5) ◽  
pp. 241-246 ◽  
Author(s):  
Zhi-Zhong Chen


1970 ◽  
Vol 13 (4) ◽  
pp. 515-517 ◽  
Author(s):  
J. Sedláček

Let G be a finite connected graph without loops or multiple edges. A maximal tree subgraph T of G is called a spanning tree of G. Denote by k(G) the number of all trees spanning the graph G. A. Rosa formulated the following problem (private communication): Let x(≠2) be a given positive integer and denote by α(x) the smallest positive integer y having the following property: There exists a graph G on y vertices with x spanning trees. Investigate the behavior of the function α(x).



1970 ◽  
Vol 11 (3) ◽  
pp. 379-380 ◽  
Author(s):  
S. B. Rao

We consider only graphs without loops or multiple edges. Pertinent definitions are given below. For notation and other definitions we generally follow Ore [1].A connected graph G = (X, E) is said to have the property P if for every maximal tree T of G there exists a vertex aT of G such that distance between aT and x is same in T as in G for every x in X. The following problem has been posed by Ore (see [1] page 103, problem 4): Determine the graphs with property P. This paper presents a solution to the above problem in the finite case.



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