Araştırma Makalesi
BibTex RIS Kaynak Göster
Yıl 2019, Cilt: 2 Sayı: 3, 206 - 212, 30.09.2019
https://doi.org/10.33434/cams.515711

Öz

Kaynakça

  • [1] B. E. Johnson, Cohomology in Banach algebras, Mem. Amer. Math. Soc., 127 (1972).
  • [2] M. Gromov, Volume and bounded cohomology, Publ. Math. IHES, 56 (1982), 5-100.
  • [3] R. Frigerio, Bounded cohomology of discrete groups, Amer. Math. Soc., 227 (2017).
  • [4] E. H. Brown, R. H. Szczarba, Continuous cohomology and real homotopy type, Trans. Amer. Math. Soc., 311(1) (1989), 57-106.
  • [5] L. Mdzinarishvili, Continuous singular cohomology, Georgian Math. J., 16 (2009), 321–342.
  • [6] M. A. Mostow, Continuous cohomology of spaces with two topologies, Mem. Amer. Math. Soc., 7 (1976), 1–142.
  • [7] J. D. Stasheff, Continuous cohomology of groups and classifying spaces, Bull. Amer. Math. Soc., 84(4) (1978), 513-530
  • [8] R. Frigerio, (Bounded) Continuous cohomology and Gromov’s proportionality principle, Manuscripta Math., 134(3-4) (2011), 435-474.
  • [9] N. Monod, Continuous bounded cohomology of locally compact groups, Lecture notes in Mathematics, no. 1758, Springer- Verlag, Berlin, 2001.
  • [10] R. Brooks, Some remarks on bounded cohomology, Ann. Math. Studies, 97 (1980), 53-63.
  • [11] R. I. Grigorchuk, Some results on bounded cohomology, Combinatorial and geometric group theory, Edinburgh, (1993), 111-163.
  • [12] N. V. Ivanov, Foundation of the theory of bounded cohomology, J. Soviet Math., 143 (1985), 69-109.
  • [13] M. M. Sadr, A. Pourabbas, Johnson amenability for topological semigroups, Iran. J. Sci. Technol. Trans. A Sci., 32(A2), (2010), 151-160.
  • [14] C. Löh, The Proportionality principle of simplicial volume, Diploma thesis, Universitat Munster, 2004.
  • [15] C. Löh, Measure homology and singular homology are isometrically isomorphic, Math. Z., 253 (2006), 197–218.
  • [16] A. Y. Helemskii, The homology of Banach and topological algebras, Kluwer, Dordrecht, 1989.
  • [17] V. Runde, Lectures on amenability, Lecture Notes in Mathematics, Springer-Verlag, Berlin, 2002.
  • [18] A. L. T. Paterson, Amenability, Amer. Math. Soc. Providence, 1978.
  • [19] V. A. Faiziev, Pseudocharacters on a free group and some group constructions, Russian Math. Surveys, 43 (1988), 225-226.
  • [20] Y. Choi, Cohomology of commutative Banach algebras and `-semigroup algebras, Ph.D. thesis, University of Newcastle upon Tyne, 2006.
  • [21] M. R. Bridson, A. Haefliger, Metric spaces of non positive curvature, Springer-Verlag, 1999.

On the Cohomology of Topological Semigroups

Yıl 2019, Cilt: 2 Sayı: 3, 206 - 212, 30.09.2019
https://doi.org/10.33434/cams.515711

Öz

In this short note, we give some new results on continuous bounded cohomology groups of topological semigroups with values in complex field. We show that the second continuous bounded cohomology group of a compact metrizable semigroup, is a Banach space. Also, we study cohomology groups of amenable topological semigroups, and we show that cohomology groups of rank greater than one of a compact left or right amenable semigroup, are trivial. Also, we give some examples and applications about topological lattices.

Kaynakça

  • [1] B. E. Johnson, Cohomology in Banach algebras, Mem. Amer. Math. Soc., 127 (1972).
  • [2] M. Gromov, Volume and bounded cohomology, Publ. Math. IHES, 56 (1982), 5-100.
  • [3] R. Frigerio, Bounded cohomology of discrete groups, Amer. Math. Soc., 227 (2017).
  • [4] E. H. Brown, R. H. Szczarba, Continuous cohomology and real homotopy type, Trans. Amer. Math. Soc., 311(1) (1989), 57-106.
  • [5] L. Mdzinarishvili, Continuous singular cohomology, Georgian Math. J., 16 (2009), 321–342.
  • [6] M. A. Mostow, Continuous cohomology of spaces with two topologies, Mem. Amer. Math. Soc., 7 (1976), 1–142.
  • [7] J. D. Stasheff, Continuous cohomology of groups and classifying spaces, Bull. Amer. Math. Soc., 84(4) (1978), 513-530
  • [8] R. Frigerio, (Bounded) Continuous cohomology and Gromov’s proportionality principle, Manuscripta Math., 134(3-4) (2011), 435-474.
  • [9] N. Monod, Continuous bounded cohomology of locally compact groups, Lecture notes in Mathematics, no. 1758, Springer- Verlag, Berlin, 2001.
  • [10] R. Brooks, Some remarks on bounded cohomology, Ann. Math. Studies, 97 (1980), 53-63.
  • [11] R. I. Grigorchuk, Some results on bounded cohomology, Combinatorial and geometric group theory, Edinburgh, (1993), 111-163.
  • [12] N. V. Ivanov, Foundation of the theory of bounded cohomology, J. Soviet Math., 143 (1985), 69-109.
  • [13] M. M. Sadr, A. Pourabbas, Johnson amenability for topological semigroups, Iran. J. Sci. Technol. Trans. A Sci., 32(A2), (2010), 151-160.
  • [14] C. Löh, The Proportionality principle of simplicial volume, Diploma thesis, Universitat Munster, 2004.
  • [15] C. Löh, Measure homology and singular homology are isometrically isomorphic, Math. Z., 253 (2006), 197–218.
  • [16] A. Y. Helemskii, The homology of Banach and topological algebras, Kluwer, Dordrecht, 1989.
  • [17] V. Runde, Lectures on amenability, Lecture Notes in Mathematics, Springer-Verlag, Berlin, 2002.
  • [18] A. L. T. Paterson, Amenability, Amer. Math. Soc. Providence, 1978.
  • [19] V. A. Faiziev, Pseudocharacters on a free group and some group constructions, Russian Math. Surveys, 43 (1988), 225-226.
  • [20] Y. Choi, Cohomology of commutative Banach algebras and `-semigroup algebras, Ph.D. thesis, University of Newcastle upon Tyne, 2006.
  • [21] M. R. Bridson, A. Haefliger, Metric spaces of non positive curvature, Springer-Verlag, 1999.
Toplam 21 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Matematik
Bölüm Articles
Yazarlar

Maysam Maysami Sadr 0000-0003-0747-4180

Danial Bouzarjomehri Amnieh Bu kişi benim 0000-0002-0883-6510

Yayımlanma Tarihi 30 Eylül 2019
Gönderilme Tarihi 21 Ocak 2019
Kabul Tarihi 29 Temmuz 2019
Yayımlandığı Sayı Yıl 2019 Cilt: 2 Sayı: 3

Kaynak Göster

APA Maysami Sadr, M., & Bouzarjomehri Amnieh, D. (2019). On the Cohomology of Topological Semigroups. Communications in Advanced Mathematical Sciences, 2(3), 206-212. https://doi.org/10.33434/cams.515711
AMA Maysami Sadr M, Bouzarjomehri Amnieh D. On the Cohomology of Topological Semigroups. Communications in Advanced Mathematical Sciences. Eylül 2019;2(3):206-212. doi:10.33434/cams.515711
Chicago Maysami Sadr, Maysam, ve Danial Bouzarjomehri Amnieh. “On the Cohomology of Topological Semigroups”. Communications in Advanced Mathematical Sciences 2, sy. 3 (Eylül 2019): 206-12. https://doi.org/10.33434/cams.515711.
EndNote Maysami Sadr M, Bouzarjomehri Amnieh D (01 Eylül 2019) On the Cohomology of Topological Semigroups. Communications in Advanced Mathematical Sciences 2 3 206–212.
IEEE M. Maysami Sadr ve D. Bouzarjomehri Amnieh, “On the Cohomology of Topological Semigroups”, Communications in Advanced Mathematical Sciences, c. 2, sy. 3, ss. 206–212, 2019, doi: 10.33434/cams.515711.
ISNAD Maysami Sadr, Maysam - Bouzarjomehri Amnieh, Danial. “On the Cohomology of Topological Semigroups”. Communications in Advanced Mathematical Sciences 2/3 (Eylül 2019), 206-212. https://doi.org/10.33434/cams.515711.
JAMA Maysami Sadr M, Bouzarjomehri Amnieh D. On the Cohomology of Topological Semigroups. Communications in Advanced Mathematical Sciences. 2019;2:206–212.
MLA Maysami Sadr, Maysam ve Danial Bouzarjomehri Amnieh. “On the Cohomology of Topological Semigroups”. Communications in Advanced Mathematical Sciences, c. 2, sy. 3, 2019, ss. 206-12, doi:10.33434/cams.515711.
Vancouver Maysami Sadr M, Bouzarjomehri Amnieh D. On the Cohomology of Topological Semigroups. Communications in Advanced Mathematical Sciences. 2019;2(3):206-12.

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