Domination between different products and finiteness of associated semi-norms

• Autores: Christoforos Neofytidis
• Localización: Publicacions matematiques, ISSN 0214-1493, Vol. 64, Nº 2, 2020, págs. 653-660
• Idioma: inglés
• DOI: 10.5565/publmat6422011
• Enlaces
  • Texto completo  1    2  
• Resumen

  • In this note we determine all possible dominations between different products of manifolds when none of the factors of the codomain is dominated byproducts. As a consequence, we determine the finiteness of every product-associated functorial semi-norm on the fundamental classes of the afore mentioned products. These results give partial answers to questions of M. Gromov.

• Referencias bibliográficas
  • S. Eilenberg, On the problems of topology, Ann. of Math. (2) 50(2) (1949),247- 260. DOI: 10.2307/1969448.
  • M. Gromov, \Metric Structures for Riemannian and Non-Riemannian Spaces",Based on the 1981 French original, With appendices by M. Katz,...
  • D. Kotschick and C. Löh, Fundamental classes not representable by products,J. Lond. Math. Soc. (2) 79(3) (2009), 545-561. DOI: 10.1112/jlms/jdn089.
  • D. Kotschick and C. Löh, Groups not presentable by products, Groups Geom.Dyn. 7(1) (2013), 181-204. DOI: 10.4171/GGD/180.
  • D. Kotschick, C. Löh, and C. Neofytidis, On stability of non-dominationunder taking products, Proc. Amer. Math. Soc. 144(6) (2016), 2705-2710.DOI:...
  • D. Kotschick and C. Neofytidis, On three-manifolds dominated by circle bundles,Math. Z. 274(1-2) (2013), 21-32. DOI: 10.1007/s00209-012-1055-3.
  • C. Neofytidis, Fundamental groups of aspherical manifolds and maps of non-zerodegree, Groups Geom. Dyn. 12(2) (2018), 637-677. DOI: 10.4171/GGD/451.
  • R. Thom, Quelques propri_et_es globales des vari_et_es di__erentiables, Comment.Math. Helv. 28 (1954), 17-86.