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

The capacity of some classes of polyhedra

Sayfa
96–105
Yayın Tarihi
2022-10-18
DOI
—
🏛️Bu makalenin bibliyografik verileri ve tam metin bağlantısı DergiPark üzerinden sağlanmıştır.
DergiPark Kaydı ↗
✨

Yapay Zeka Hızlı Bakış & Çıkarımlar

AI Insight
⚡ TL;DR(1 Cümlede Hızlı Çıkarım)

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 Maddede Bu Makale

🎯
Amaç & Hipotez:Borsuk in 1979, in Topological Conference in Moscow, introduced the concept of the capacity of a compactum.
📊
Temel Bulgular & Veri: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.
💡
Sonuç & Katkı: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 $\mathbb{Z}_n$.
🔬Tür:Araştırma Makalesi
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler: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 $\mathbb{Z}_n$.

🔖

Bu Makaleye Atıf Yap

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

📄 Tam Metin PDF Okuyucu

📄

PDF görüntüleyici hazırlanıyor...

Kaynakça (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.