In low-dimensional topology, the trigenus of a closed 3-manifold is an invariant consisting of an ordered triple . It is obtained 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 withfor and being the genus of . For orientable spaces, ,where is 's Heegaard genus. For non-orientable spaces the has the form depending on theimage of the first Stiefel–Whitney characteristic class under a Bockstein homomorphism, respectively for
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| - In low-dimensional topology, the trigenus of a closed 3-manifold is an invariant consisting of an ordered triple . It is obtained 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 withfor and being the genus of . For orientable spaces, ,where is 's Heegaard genus. For non-orientable spaces the has the form depending on theimage of the first Stiefel–Whitney characteristic class under a Bockstein homomorphism, respectively for (en)
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| - In low-dimensional topology, the trigenus of a closed 3-manifold is an invariant consisting of an ordered triple . It is obtained 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 withfor and being the genus of . For orientable spaces, ,where is 's Heegaard genus. For non-orientable spaces the has the form depending on theimage of the first Stiefel–Whitney characteristic class under a Bockstein homomorphism, respectively for It has been proved that the number has a relation with the concept of , that is, an orientable surface which is embedded in , has minimal genus and represents the first Stiefel–Whitney class under the duality map , that is, . If then , and if then . (en)
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