Index Function and Minimal Cycles

2005/10/21 by Lapteva, A. V., Yakovlev, E. I.
#57N65 #57Q15 #65D18 #Algebraic Topology (math.AT) #FOS: Mathematics

paper · doi:10.48550/arxiv.math/0510458

Abstract

Let P be a closed triangulated manifold, dim P=n. We consider the group of simplicial 1-chains C₁(P) and the homology group H₁(P). We also use some nonnegative weighting function L on C₁(P). For any homological class from H₁(P) method proposed in article builds a cycle z with minimal weight L(z). The main idea is in using a simplicial scheme of space of the regular covering with automorphism group H₁(P). We construct this covering applying index function relative to any basis of group H_n-1(P).

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