Strong surjectivity of maps from 2-complexes into the 2-sphere

• Autorzy: Marcio Fenille , Oziride Neto
• Języki publikacji: EN

Abstrakty

EN

Given a model 2-complex K P of a group presentation P, we associate to it an integer matrix ΔP and we prove that a cellular map f: K P → S 2 is root free (is not strongly surjective) if and only if the diophantine linear system ΔP Y = $$ \overrightarrow {deg} $$(f) has an integer solution, here $$ \overrightarrow {deg} $$(f)is the so-called vector-degree of f

Słowa kluczowe

EN

Strong surjectivity; Two-dimensional complexes; Group presentation; Diophantine linear system

• Wydawca: De Gruyter Open
• Czasopismo: Open Mathematics
• Rocznik: 2010
• Tom: 8
• Numer: 3
• Strony: 421-429

Daty

wydano

2010-06-01

online

2010-05-30

Twórcy

autor

Marcio Fenille

• Universidade Federal de Itajubá,

autor

Oziride Neto

• Universidade de São Paulo,

Bibliografia

• [1] Aniz C., Strong surjectivity of mappings of some 3-complexes into 3-manifolds, Fund. Math., 2006, 192(3), 195–214 http://dx.doi.org/10.4064/fm192-3-1
• [2] Aniz C., Strong surjectivity of mappings of some 3-complexes into \( M_{Q_8 } \) , Cent. Eur. J. Math., 2008, 6(4), 497–503 http://dx.doi.org/10.2478/s11533-008-0042-8
• [3] Brooks R., Nielsen root theory, In: Handbook of Topological Fixed Point Theory, Springer, Dordrecht, 2005, 375–431 http://dx.doi.org/10.1007/1-4020-3222-6_11
• [4] Ching W.S., Linear equation over commutative rings, Linear Algebra and Appl., 1977, 18(3), 257–266 http://dx.doi.org/10.1016/0024-3795(77)90055-6
• [5] Gonçalves D.L., Coincidence theory for maps from a complex into a manifold, Topology Appl., 1999, 92(1), 63–77 http://dx.doi.org/10.1016/S0166-8641(97)00231-9
• [6] Gonçalves D.L., Coincidence theory, In: Handbook of Topological Fixed Point Theory, Springer, Dordrecht, 2005, 3–42 http://dx.doi.org/10.1007/1-4020-3222-6_1
• [7] Gonçalves D.L., Wong P., Wecken property for roots, Proc. Amer. Math. Soc., 2005, 133(9), 2779–2782 http://dx.doi.org/10.1090/S0002-9939-05-07820-2
• [8] Hu S.T., Homotopy Theory, Academic Press, New York-London, 1959
• [9] Munkres J.R., Topology, 2nd ed., Princeton Hall, Upper Saddle River, 2000
• [10] Sieradski A.J., Algebraic topology for two-dimensional complexes, In: Two-dimensional Homotopy and Combinatorial Group Theory, London Mathematical Society Lecture Notes Series, 197, Cambridge University Press, Cambridge, 1993, 51–96 http://dx.doi.org/10.1017/CBO9780511629358.004

Identyfikatory

DOI

10.2478/s11533-010-0031-6