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Hurewicz and Poincare Theorems for Simplicial Modules

Year 2022, Volume: 5 Issue: 2, 81 - 88, 01.06.2022
https://doi.org/10.33401/fujma.1031108

Abstract

We will give the simplicial analogues of Hurewicz and Poincaré theorems as an application of simplicial homology and homotopy.

References

  • [1] J. C. Moore, Homotopie des Complexes Mon¨oideaux, Seminaire Henri Cartan, 1954.
  • [2] J. W. Milnor, The geometric realization of a semi-simplicial complex, Ann. of Math., 2 (65) (1957), 357-362.
  • [3] M. Andre, Homologie des Algebres Commutatives, Springer-Verlag, 1970.
  • [4] D. Quillen, Higher algebraic K-theory, Proc. Seattle Lec., Notes Math., Springer, 341 (1973), 85-147.
  • [5] Z. Arvasi, T. Porter, Higher dimensional peiffer elements in simplicial commutative algebras, Theory Appl. Categ., 3 (1997), 1-23.
  • [6] Z. Arvasi, T. Porter, Simplicial and crossed resolutions of commutative algebra, J. Algebra, 181 (1996), 426-448.
  • [7] J. Wu, Simplicial objects and homotopy groups, Lecture Notes Series Institute for Mathematical Sciences, National University of Singapore, World scientific, 19 (2010), 31-183.
  • [8] E. B. Curtis, Simplicial homotopy theory, Adv. Math., 6 (1971), 107-209.
  • [9] P. G. Goerss, J. F. Jardine, Simplicial Homotopy Theory: Progress in Mathematics, Birkhauser, Basel-Boston-Berlin, 1999.
  • [10] J. P. May, Simplicial Objects in Algebraic Topology, Mathematic Studies 11, Van Nostrand, 1967.
Year 2022, Volume: 5 Issue: 2, 81 - 88, 01.06.2022
https://doi.org/10.33401/fujma.1031108

Abstract

References

  • [1] J. C. Moore, Homotopie des Complexes Mon¨oideaux, Seminaire Henri Cartan, 1954.
  • [2] J. W. Milnor, The geometric realization of a semi-simplicial complex, Ann. of Math., 2 (65) (1957), 357-362.
  • [3] M. Andre, Homologie des Algebres Commutatives, Springer-Verlag, 1970.
  • [4] D. Quillen, Higher algebraic K-theory, Proc. Seattle Lec., Notes Math., Springer, 341 (1973), 85-147.
  • [5] Z. Arvasi, T. Porter, Higher dimensional peiffer elements in simplicial commutative algebras, Theory Appl. Categ., 3 (1997), 1-23.
  • [6] Z. Arvasi, T. Porter, Simplicial and crossed resolutions of commutative algebra, J. Algebra, 181 (1996), 426-448.
  • [7] J. Wu, Simplicial objects and homotopy groups, Lecture Notes Series Institute for Mathematical Sciences, National University of Singapore, World scientific, 19 (2010), 31-183.
  • [8] E. B. Curtis, Simplicial homotopy theory, Adv. Math., 6 (1971), 107-209.
  • [9] P. G. Goerss, J. F. Jardine, Simplicial Homotopy Theory: Progress in Mathematics, Birkhauser, Basel-Boston-Berlin, 1999.
  • [10] J. P. May, Simplicial Objects in Algebraic Topology, Mathematic Studies 11, Van Nostrand, 1967.
There are 10 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Articles
Authors

Elif Ilgaz Çağlayan 0000-0002-4202-6570

Publication Date June 1, 2022
Submission Date December 1, 2021
Acceptance Date February 25, 2022
Published in Issue Year 2022 Volume: 5 Issue: 2

Cite

APA Ilgaz Çağlayan, E. (2022). Hurewicz and Poincare Theorems for Simplicial Modules. Fundamental Journal of Mathematics and Applications, 5(2), 81-88. https://doi.org/10.33401/fujma.1031108
AMA Ilgaz Çağlayan E. Hurewicz and Poincare Theorems for Simplicial Modules. Fundam. J. Math. Appl. June 2022;5(2):81-88. doi:10.33401/fujma.1031108
Chicago Ilgaz Çağlayan, Elif. “Hurewicz and Poincare Theorems for Simplicial Modules”. Fundamental Journal of Mathematics and Applications 5, no. 2 (June 2022): 81-88. https://doi.org/10.33401/fujma.1031108.
EndNote Ilgaz Çağlayan E (June 1, 2022) Hurewicz and Poincare Theorems for Simplicial Modules. Fundamental Journal of Mathematics and Applications 5 2 81–88.
IEEE E. Ilgaz Çağlayan, “Hurewicz and Poincare Theorems for Simplicial Modules”, Fundam. J. Math. Appl., vol. 5, no. 2, pp. 81–88, 2022, doi: 10.33401/fujma.1031108.
ISNAD Ilgaz Çağlayan, Elif. “Hurewicz and Poincare Theorems for Simplicial Modules”. Fundamental Journal of Mathematics and Applications 5/2 (June 2022), 81-88. https://doi.org/10.33401/fujma.1031108.
JAMA Ilgaz Çağlayan E. Hurewicz and Poincare Theorems for Simplicial Modules. Fundam. J. Math. Appl. 2022;5:81–88.
MLA Ilgaz Çağlayan, Elif. “Hurewicz and Poincare Theorems for Simplicial Modules”. Fundamental Journal of Mathematics and Applications, vol. 5, no. 2, 2022, pp. 81-88, doi:10.33401/fujma.1031108.
Vancouver Ilgaz Çağlayan E. Hurewicz and Poincare Theorems for Simplicial Modules. Fundam. J. Math. Appl. 2022;5(2):81-8.

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