Highlights? Linear time algorithm to cohomology generators computations for orientable open and closed 2d manifolds is presented. ? Extension to optimal cohomology generators is given. ? Some extension to non-manifold cases are provided. In this paper a fast algorithm to compute cohomology group generators of cellular decomposition of any orientable open or closed 2-manifold is described. The presented algorithm is a dual version of algorithm to compute homology generators presented by David Eppstein in "Dynamic generators of topologically embedded graphs" and developed by Jeff Erickson and Kim Whittlesey in "Greedy optimal homotopy and homology generators". Some parts of the paper bases on ideas presented in "Optimal discrete Morse functions for 2-manifolds" by Thomas Lewiner, Helio Lopes and Geovan Tavares. Extension of the algorithm to some non-manifold cases is provided.
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A fast algorithm to compute cohomology group generators of orientable 2-manifolds
Semantic Scholar · Mathematics · 2012
Abstract
Highlights? Linear time algorithm to cohomology generators computations for orientable open and closed 2d manifolds is presented. ? Extension to optimal cohomology generators is given. ? Some extension to non-manifold cases are provided. In this paper a fast algorithm to compute cohomology group generators of cellular decomposition of any orientable open or closed 2-manifold is described. The presented algorithm is a dual version of algorithm to compute homology generators presented by David Eppstein in "Dynamic generators of topologically embedded graphs" and developed by Jeff Erickson and Kim Whittlesey in "Greedy optimal homotopy and homology generators". Some parts of the paper bases on ideas presented in "Optimal discrete Morse functions for 2-manifolds" by Thomas Lewiner, Helio Lopes and Geovan Tavares. Extension of the algorithm to some non-manifold cases is provided.