Freedman
Daniel
Daniel Freedman
Chen
Chao
Chao Chen
2008
We develop a method for measuring homology classes. This involves
three problems. First, we define the size of a homology class,
using ideas from relative homology. Second, we define an optimal
basis of a homology group to be the basis whose elements' size have
the minimal sum. We provide a greedy algorithm to compute the
optimal basis and measure classes in it. The algorithm runs in
$O(\beta^4 n^3 log^2 n)$ time, where $n$ is the size of the
simplicial complex and $\beta$ is the Betti number of the homology
group. Third, we discuss different ways of localizing homology
classes and prove some hardness results.
eng
Computer Science, 000 Computer science, knowledge, general works
Quantifying Homology Classes
Schloss Dagstuhl - Leibniz-Zentrum fuer Informatik GmbH, Wadern/Saarbruecken, Germany