Codes

TopoS2 is a specialized software written for computing the topology of scalar functions on S2, especially adapted to the HealPix data format. It is written in the context of the topological analysis of Planck CMB maps, however useful for other scalar functions on S2. Its usage in the context of Planck data is documented in the following paper:

• P. Pranav. Anomalies in the topology of the temperature fluctuations in the cosmic microwave background: An analysis of the NPIPE and FFP10 datasets. Astronomy & Astrophysics 659, A115, (2022).
  [DOI: 10.1051/0004-6361/202140291]

The documentation for usage beyond HealPix and Planck data will be updated at a future stage. The topological summary data (15GB tarball) in terms of persisatence diagrams and Betti numbers, computed via relative homology, for the Planck datasets analyzed in the above paper, are publicly hosted here, in the hope that they will be useful for the wider community.

Also see these papers for a case study of TopoS2:

• P. Pranav, R. J. Adler, T. Buchert, H. Edelsbrunner, B. J. T. Jones, A. Schwartzman, H. Wagner, and R. Van de Weygaert,. Unexpected topology of the temperature fluctuations in the cosmic microwave background. Astronomy & Astrophysics, 627, A163 (2019). [Paper]


• P. Pranav. Loops abound in the cosmic microwave background. arXiv preprint , arXiv:2101.02237 (2021). [Paper]

I worked with Nitin Shivshankar during PhD to develop a semi-automatic filament finder FELIX. The software allows greater control over selection by allowing density range based identification of filamentrary structures in hierarchical settings. See this paper for a case study.

Additionally, there are a variety of codes available for topological computations for 2D and 3D regular grids in the public domain (e.g. DIONYSUS, DIPHA, GUDHI, PHAT).