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1. | Department of Mathematics, Rutgers University, Piscataway, NJ 08854, United States |
2. | Rutgers University, 110 Frelinghusen Road, Piscataway, NJ 08854, United States |
3. | Department of Mathematics, University of Pennsylvania, Philadelphia, PA 19104, United States |
References:
[1] |
A. Bjorner, Nerves, fibers and homotopy groups, Journal of Combinatorial Theory, Series A, 102 (2003), 88-93.
doi: 10.1016/S0097-3165(03)00015-3. |
[2] |
K. Borsuk, On the imbedding of systems of compacta in simplicial complexes, Fundamenta Mathematicae, 35 (1948), 217-234. |
[3] |
G. Carlsson, Topology and data, Bulletin of the American Mathematical Society, 46 (2009), 255-308.
doi: 10.1090/S0273-0979-09-01249-X. |
[4] |
J.-G. Dumas, F. Heckenbach, B. D. Saunders and V. Welker, Computing simplicial homology based on efficient Smith normal form algorithms, Proceedings of Algebra, Geometry and Software Systems, (2003), 177-206. |
[5] |
H. Edelsbrunner and J. L. Harer, Computational Topology - an Introduction, American Mathematical Society, Providence, RI, 2010. |
[6] |
K. Fischer, B. Gaertner and M. Kutz, Fast-smallest-enclosing-ball computation in high dimensions, Proceedings of the $11^{th}$ Annual European Symposium on Algorithms (ESA), 2832 (2003), 630-641.
doi: 10.1007/978-3-540-39658-1_57. |
[7] |
R. Ghrist, Three examples of applied and computational homology, Nieuw Archief voor Wiskunde, 9 (2008), 122-125. |
[8] |
A. Granas and J. Dugundji, Fixed Point Theory, Springer-Verlag, New York, 2003.
doi: 10.1007/978-0-387-21593-8. |
[9] |
S. Harker, K. Mischaikow, M. Mrozek and V. Nanda, Discrete Morse theoretic algorithms for computing homology of complexes and maps, Foundations of Computational Mathematics, 14 (2014), 151-184.
doi: 10.1007/s10208-013-9145-0. |
[10] |
T. Kaczynski, K. Mischaikow and M. Mrozek, Computational Homology, Springer-Verlag, New York, 2004.
doi: 10.1007/b97315. |
[11] |
D. Kozlov, Combinatorial Algebraic Topology, Springer, 2008.
doi: 10.1007/978-3-540-71962-5. |
[12] |
J. R. Munkres, Elements of Algebraic Topology, Addison-Wesley, Menlo Park, 1984. |
[13] |
P. Niyogi, S. Smale and S. Weinberger, Finding the homology of submanifolds with high confidence from random samples, Discrete and Computational Geometry, 39 (2008), 419-441.
doi: 10.1007/s00454-008-9053-2. |
[14] |
S. Smale, A Vietoris mapping theorem for homotopy, Proceedings of the American mathematical society, 8 (1957), 604-610.
doi: 10.1090/S0002-9939-1957-0087106-9. |
[15] |
E. H. Spanier, Algebraic Topology, Springer-Verlag, New York, 1981. Corrected reprint. |
show all references
References:
[1] |
A. Bjorner, Nerves, fibers and homotopy groups, Journal of Combinatorial Theory, Series A, 102 (2003), 88-93.
doi: 10.1016/S0097-3165(03)00015-3. |
[2] |
K. Borsuk, On the imbedding of systems of compacta in simplicial complexes, Fundamenta Mathematicae, 35 (1948), 217-234. |
[3] |
G. Carlsson, Topology and data, Bulletin of the American Mathematical Society, 46 (2009), 255-308.
doi: 10.1090/S0273-0979-09-01249-X. |
[4] |
J.-G. Dumas, F. Heckenbach, B. D. Saunders and V. Welker, Computing simplicial homology based on efficient Smith normal form algorithms, Proceedings of Algebra, Geometry and Software Systems, (2003), 177-206. |
[5] |
H. Edelsbrunner and J. L. Harer, Computational Topology - an Introduction, American Mathematical Society, Providence, RI, 2010. |
[6] |
K. Fischer, B. Gaertner and M. Kutz, Fast-smallest-enclosing-ball computation in high dimensions, Proceedings of the $11^{th}$ Annual European Symposium on Algorithms (ESA), 2832 (2003), 630-641.
doi: 10.1007/978-3-540-39658-1_57. |
[7] |
R. Ghrist, Three examples of applied and computational homology, Nieuw Archief voor Wiskunde, 9 (2008), 122-125. |
[8] |
A. Granas and J. Dugundji, Fixed Point Theory, Springer-Verlag, New York, 2003.
doi: 10.1007/978-0-387-21593-8. |
[9] |
S. Harker, K. Mischaikow, M. Mrozek and V. Nanda, Discrete Morse theoretic algorithms for computing homology of complexes and maps, Foundations of Computational Mathematics, 14 (2014), 151-184.
doi: 10.1007/s10208-013-9145-0. |
[10] |
T. Kaczynski, K. Mischaikow and M. Mrozek, Computational Homology, Springer-Verlag, New York, 2004.
doi: 10.1007/b97315. |
[11] |
D. Kozlov, Combinatorial Algebraic Topology, Springer, 2008.
doi: 10.1007/978-3-540-71962-5. |
[12] |
J. R. Munkres, Elements of Algebraic Topology, Addison-Wesley, Menlo Park, 1984. |
[13] |
P. Niyogi, S. Smale and S. Weinberger, Finding the homology of submanifolds with high confidence from random samples, Discrete and Computational Geometry, 39 (2008), 419-441.
doi: 10.1007/s00454-008-9053-2. |
[14] |
S. Smale, A Vietoris mapping theorem for homotopy, Proceedings of the American mathematical society, 8 (1957), 604-610.
doi: 10.1090/S0002-9939-1957-0087106-9. |
[15] |
E. H. Spanier, Algebraic Topology, Springer-Verlag, New York, 1981. Corrected reprint. |
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