Special Lecture Algorithms and software of the cubical homology computation. -Part1 Introduction-

Date
2006-11-07 16:30 - 2006-11-07 17:30
Place
Faculty of Science Building #3 Room 508
Speaker/Organizer
Pawel Pilarczyk(Kyoto University)
 
In the first talk, a brief introduction to the homology of topological spaces will be given, and the approach to the computation of homology based on cubes as opposed to simplices (which are typically used in the algebraic topology courses) will be described. The Computational Homology Project (CHomP) and its freely available software will also be introduced; this software works directly with cubical structures (pixels, voxels), which is most suitable to process digital data. This talk is intended for general mathematical audience and no prior knowledge of algebraic topology will be required. In the second talk, various technical details of the homology computation will be discussed. Geometric and algebraic reduction techniques of the cubical data will be described, homology computation of maps will be introduced, and some specific applications will be pointed out. Technical aspects of using the software available at the CHomP website http://www.math.gatech.edu/~chomp/ will also be discussed.