Freedman
Daniel
Daniel Freedman
Chen
Chao
Chao Chen
12 pages
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.
Editor
Herbstritt
Marc
Marc Herbstritt
https://doi.org/10.4230/lipics.stacs.2008.1343
eng
Computer Science, 000 Computer science, knowledge, general works
Quantifying Homology Classes
DataCite
Schloss Dagstuhl - Leibniz-Zentrum fuer Informatik GmbH, Wadern/Saarbruecken, Germany