Dualities in Persistent (Co)Homology [electronic resource]

• Ngôn ngữ: eng
• Ký hiệu phân loại: 333.79 Energy
• Thông tin xuất bản: Berkeley, Calif. : Oak Ridge, Tenn. : Lawrence Berkeley National Laboratory ; Distributed by the Office of Scientific and Technical Information, U.S. Dept. of Energy, 2011
• Mô tả vật lý: Medium: ED : , digital, PDF file.
• Bộ sưu tập: Metadata
• ID: 268466
• Chủ đề: 1. 01 coal, lignite, and peat; 2. 97 mathematics and computing

Tóm tắt

We consider sequences of absolute and relative homology and cohomology groups that arise naturally for a filtered cell complex. We establishalgebraic relationships between their persistence modules, and show that they contain equivalent information. We explain how one can use the existingalgorithm for persistent homology to process any of the four modules, and relate it to a recently introduced persistent cohomology algorithm. Wepresent experimental evidence for the practical efficiency of the latter algorithm.