Trigenus
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High Quality Content by WIKIPEDIA articles! In low-dimensional topology, the trigenus is an invariant consisting of a triplet (g1,g2,g3) assigned to closed 3-manifolds. The definition is by minimizing the genera of three orientable handle bodies with no intersection between their interiors which decompose the manifold as far as the Heegaard genus need only two. That is, a decomposition into scriptstyle M=V1cup V2cup V3 with scriptstyle {rm int} Vicap {rm int} Vj=varnothing for i,j = 1,2,3 and being gi the genus of Vi. For orientable spaces scriptstyle {rm trig}(M)=(0,0,h) where h is M's Heegaard genus. For non-orientable spaces the trig has the form as scriptstyle {rm trig}(M)=(0,g2,g3)quad mbox{or}quad (1,g2,g3) depending on the image of the first Stiefel-Whitney characteristic class w1 under a Bockstein homomorphism, respectively for scriptstyle beta(w1)=0quad mbox{or}quad neq 0.
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GarantieWeitere Informationen
- Allgemeine Informationen
- GTIN 09786131142789
- Editor Lambert M. Surhone, Miriam T. Timpledon, Susan F. Marseken
- EAN 9786131142789
- Format Fachbuch
- Titel Trigenus
- Herausgeber Betascript Publishing
- Anzahl Seiten 68
- Genre Mathematik
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