SavedAdd your journal

Journals / Hacettepe Journal of Mathematics and Statistics / 2020 / Cilt: 49 - Sayı: 1

The capacity of some classes of polyhedra

Behrooz MASHAYEKHY
Hanieh MİREBRAHİMİ
Mojtaba MOHARERİ
Pages
96–105
Publication Date
2022-10-18
DOI
—
🏛️Bibliographic metadata and full text access for this article are provided via DergiPark.
DergiPark Record ↗
✨

AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

Also, we present an upper bound for the capacity of a $\mathbb{Z}_n$-complex, i.e., a connected finite 2-dimensional CW-complex with finite cyclic fundamental group $\mathbb{Z}_n$.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:Borsuk in 1979, in Topological Conference in Moscow, introduced the concept of the capacity of a compactum.
📊
Key Findings & Data:In this paper, we compute the capacity of the product of two spheres of the same or different dimensions and the capacity of lense spaces.
💡
Conclusion & Impact:Also, we present an upper bound for the capacity of a $\mathbb{Z}_n$-complex, i.e., a connected finite 2-dimensional CW-complex with finite cyclic fundamental group $\mathbb{Z}_n$.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:homotopy domination · homotopy type · Moore space

Abstract

K. Borsuk in 1979, in Topological Conference in Moscow, introduced the concept of the capacity of a compactum. In this paper, we compute the capacity of the product of two spheres of the same or different dimensions and the capacity of lense spaces. Also, we present an upper bound for the capacity of a $\mathbb{Z}_n$-complex, i.e., a connected finite 2-dimensional CW-complex with finite cyclic fundamental group $\mathbb{Z}_n$.

🔖

Cite This Article

MASHAYEKHY, B., MİREBRAHİMİ, H., MOHARERİ, M. (2022). The capacity of some classes of polyhedra. Hacettepe Journal of Mathematics and Statistics, Cilt: 49 - Sayı: 1, 96–105. https://ajindex.com/articles/529665

📄 Full Text PDF Viewer

📄

PDF görüntüleyici hazırlanıyor...

References (21)

  1. M. Abbasi and B. Mashayekhy, On the capacity and depth of compact surfaces, arXiv:1612.03335v1
  2. H.J. Baues, Combinatorial homotopy and 4-dimensional complexes, De Gruyter, vol. 2, Berlin, 1991
  3. H.J. Baues, Homotopy Type and Homology, Oxford University Press Inc., New York, 1996
  4. I. Berstein and T. Ganea, Remark on spaces dominated by manifolds, Fund. Math. 47, 45–56, 1959
  5. K. Borsuk, Some problems in the theory of shape of compacta, Russian Math. Surveys, 34 (6), 24–26, 1979
  6. J.M. Cohen, Complexes dominated by a 2-complex, Topology, 16, 409–415, 1977
  7. M.N. Dyer and A.J. Sieradski, Trees of homotopy types of two-dimensional CWcomplexes, Comment. Math. Helv. 48, 31–44, 1973
  8. A. Hatcher, Algebraic Topology, Cambridge University Press, 2002
  9. A. Hatcher, The Classification of 3-Manifolds - A Brief Overview, https://pi.math.cornell.edu/ hatcher/Papers/3Msurvey.pdf
  10. P.J. Hilton, An Introduction to Homotopy Theory, Cambridge University Press, 1961
  11. Y. Kodama, J. Ono and T. Watanabe, AR associated with ANR-sequence and shape, General Topology Appl. 9 (7), 1–88, 1978
  12. D. Kolodziejczyk, There exists a polyhedron dominating infinitely many different homotopy types, Fund. Math. 151, 39–46, 1996
  13. D. Kolodziejczyk, Polyhedra with finite fundamental group dominate only finitely many different homotopy types, Fund. Math. 180, 1–9, 2003
  14. D. Kolodziejczyk, Polyhedra dominating finitely many different homotopy types, Topology Appl. 146-147, 583–592, 2005
  15. S. Mardesic and J. Segal, Shape Theory. The Inverse System Approach, North-Holland Mathematical Library, vol. 26, North-Holland, Amsterdam, 1982
  16. M. Mather, Counting homotopy types of manifolds, Topology, 4, 93–94, 1965
  17. M. Mohareri, B. Mashayekhy and H. Mirebrahimi, On The Capacity of Eilenberg- MacLane and Moore Spaces, J. Algebraic Systems, 6 (2), 131–146, 2019
  18. M. Mohareri, B. Mashayekhy and H. Mirebrahimi, The Capacity of Wedge Sum of Spheres of Different Dimensions, Topology Appl. 246, 1–8, 2018
  19. N.E. Steenrod, The Topology of Fiber Bundles, Princeton, 1951
  20. R.G. Swan, Groups of cohomological dimension one, J. Algebra, 12, 585–601, 1969
  21. C.T.C.Wall, Finiteness conditions for CW-complexes, Ann. of Math. 81, 56–69, 1965.