Skip to main content
    • Aa
    • Aa

Frobenius n-homomorphisms, transfers and branched coverings

  • V. M. BUCHSTABER (a1), V. M. BUCHSTABER (a2) and E. G. REES (a2)

The main purpose is to characterise continuous maps that are n-branched coverings in terms of induced maps on the rings of functions. The special properties of Frobenius n-homomorphisms between two function spaces that correspond to n-branched coverings are determined completely. Several equivalent definitions of a Frobenius n-homomorphism are compared and some of their properties are proved. An axiomatic treatment of n-transfers is given in general and properties of n-branched coverings are studied and compared with those of regular coverings.

Hide All
[1]Buchstaber V. M. and Rees E. G.. The Gelfand map and symmetric products. Selecta Mathematic 8 (2002), 523535.
[2]Buchstaber V. M. and Rees E. G.. Rings of continuous functions, symmetric products and Frobenius algebras. Uspekhi Mat. Nauk 59 (2004), no. 1 (355), 125144. Translated: Russian Math. Survey 59 (2004), no. 1, 125–146.
[3]Buchstaber V. M. and Rees E. G.. Multivalued groups, their representations and Hopf algebras. Transform. Group 2 (1997), no. 4, 325349.
[4]Buchstaber V. M. and Rees E. G.. Multivalued groups, n-Hopf algebras and n-ring homomorphisms. Lie groups and Lie algebras. Math. Appl 433 (Kluwer Academic Publsher, 1998), 85107.
[5]Dold A.. Ramified coverings, orbit projections and symmetric powers. Math. Proc. Camb. Phil. Soc 99 (1986), no. 1, 6572.
[6]Gugnin D. V.. On continuous and irreducible Frobenius n-homomorphisms. Uspekhi Mat. Nauk 60 (2005), no. 5, 181182. Translated: Russian Math. Survey 60 (2005), no. 5, 967–969.
[7]Macdonald I. G.. Symmetric Functions and Hall Polynomials (Clarendon Press, 1979).
[8]Smith L.. Transfer and ramified coverings. Math. Proc. Camb. Phil. Soc 93 (1983), no. 3, 485493
[9]Steenrod N. E.. The Theory of Fiber Bundles (Princeton University Press, 1951).
Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

Mathematical Proceedings of the Cambridge Philosophical Society
  • ISSN: 0305-0041
  • EISSN: 1469-8064
  • URL: /core/journals/mathematical-proceedings-of-the-cambridge-philosophical-society
Please enter your name
Please enter a valid email address
Who would you like to send this to? *


Full text views

Total number of HTML views: 0
Total number of PDF views: 3 *
Loading metrics...

Abstract views

Total abstract views: 52 *
Loading metrics...

* Views captured on Cambridge Core between September 2016 - 21st October 2017. This data will be updated every 24 hours.