Book Review
The AMS does not provide abstracts of book reviews.
You may download the entire review from the links below.
MathSciNet review:
4274518
Full text of review:
PDF
This review is available free of charge.
Book Information:
Author:
Dmitry N. Kozlov
Title:
Organized collapse: An introduction to discrete Morse theory
Additional book information:
Graduate Studies in Mathematics, Vol. 207,
American Mathematical Society,
Providence, RI,
2020,
xxiii+312 pp.,
ISBN 978-1-4704-5701-3,
hardcover
U. Bauer, Ripser: efficient computation of Vietoris-Rips barcodes, preprint (2019), arXiv:1908.02518.
Robin Forman, Morse theory for cell complexes, Adv. Math. 134 (1998), no. 1, 90–145. MR 1612391, DOI 10.1006/aima.1997.1650
M. Jungerman and G. Ringel, Minimal triangulations on orientable surfaces, Acta Math. 145 (1980), no. 1-2, 121–154. MR 586595, DOI 10.1007/BF02414187
Henry King, Kevin Knudson, and Neža Mramor, Generating discrete Morse functions from point data, Experiment. Math. 14 (2005), no. 4, 435–444. MR 2193806
Kevin P. Knudson, Morse theory, World Scientific Publishing Co. Pte. Ltd., Hackensack, NJ, 2015. Smooth and discrete. MR 3379451, DOI 10.1142/9360
J. Milnor, Morse theory, Annals of Mathematics Studies, No. 51, Princeton University Press, Princeton, N.J., 1963. Based on lecture notes by M. Spivak and R. Wells. MR 0163331
V. Nanda, Perseus, the persistent homology software, http://www.sas.upenn.edu/~vnanda/perseus, accessed 02/01/2021.
Nicholas A. Scoville, Discrete Morse theory, Student Mathematical Library, vol. 90, American Mathematical Society, Providence, RI, 2019. MR 3970274, DOI 10.1090/stml/090
J. H. C. Whitehead, Simple homotopy types, Amer. J. Math. 72 (1950), 1–57. MR 35437, DOI 10.2307/2372133
References
- U. Bauer, Ripser: efficient computation of Vietoris-Rips barcodes, preprint (2019), arXiv:1908.02518.
- Robin Forman, Morse theory for cell complexes, Adv. Math. 134 (1998), no. 1, 90–145. MR 1612391, DOI 10.1006/aima.1997.1650
- M. Jungerman and G. Ringel, Minimal triangulations on orientable surfaces, Acta Math. 145 (1980), no. 1-2, 121–154. MR 586595, DOI 10.1007/BF02414187
- Henry King, Kevin Knudson, and Neža Mramor, Generating discrete Morse functions from point data, Experiment. Math. 14 (2005), no. 4, 435–444. MR 2193806
- Kevin P. Knudson, Morse theory: Smooth and discrete, World Scientific Publishing Co. Pte. Ltd., Hackensack, NJ, 2015. MR 3379451, DOI 10.1142/9360
- J. Milnor, Morse theory, Based on lecture notes by M. Spivak and R. Wells. Annals of Mathematics Studies, No. 51, Princeton University Press, Princeton, N.J., 1963. MR 0163331
- V. Nanda, Perseus, the persistent homology software, http://www.sas.upenn.edu/~vnanda/perseus, accessed 02/01/2021.
- Nicholas A. Scoville, Discrete Morse theory, Student Mathematical Library, vol. 90, American Mathematical Society, Providence, RI, 2019. MR 3970274, DOI 10.1090/stml/090
- J. H. C. Whitehead, Simple homotopy types, Amer. J. Math. 72 (1950), 1–57. MR 35437, DOI 10.2307/2372133
Review Information:
Reviewer:
Kevin P. Knudson
Affiliation:
Department of Mathematics, University of Florida, P.O. Box 118105, Gainesville, Florida 32611
Email:
kknudson@ufl.edu
Journal:
Bull. Amer. Math. Soc.
58 (2021), 467-473
DOI:
https://doi.org/10.1090/bull/1734
Published electronically:
March 24, 2021
Review copyright:
© Copyright 2021
American Mathematical Society
