Please use this identifier to cite or link to this item: https://doi.org/10.2140/agt.2011.11.887
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dc.titleThe intersecting kernels of heegaard splittings
dc.contributor.authorLei, F.
dc.contributor.authorWu, J.
dc.date.accessioned2014-10-28T02:47:44Z
dc.date.available2014-10-28T02:47:44Z
dc.date.issued2011
dc.identifier.citationLei, F., Wu, J. (2011). The intersecting kernels of heegaard splittings. Algebraic and Geometric Topology 11 (2) : 887-908. ScholarBank@NUS Repository. https://doi.org/10.2140/agt.2011.11.887
dc.identifier.issn14722747
dc.identifier.urihttp://scholarbank.nus.edu.sg/handle/10635/104308
dc.description.abstractLet V ∪sW be a Heegaard splitting for a closed orientable 3-manifold M. The inclusion-induced homomorphisms π1 (S) → π 1 (S)→ π 1 (W) are both surjective. The paper is principally concerned with the kernels K = Ker (π1(S) → π1 (V)), L = Ker(π1(S) → π1 (W)), their intersection K ∩ L and the quotient (K∩L)/[K,L]. The module (K ∩ L)/=[K,L] is of special interest because it is isomorphic to the second homotopy module π2(M). There are two main results. (1) We present an exact sequence of Z (π1(M)-modules of the form (K∩L)/=[K,L] {right arrow, hooked} R{xl,...,xg}/J →Tπ R{y1,...yg}→theta; R↠∈Z where R=Z(φ1(M)), J is a cyclic R-submodule of R{X1...xg}, Tθ and are explicitly described morphisms of R-modules and T involves Fox derivatives related to the gluing data of the Heegaard splitting M = V Us W. (2) Let K be the intersection kernel for a Heegaard splitting of a connected sum, and k1, K2 the intersection kernels of the two summands. We show that there is a surjection K → K1 * K2 onto the free product with kernel being normally generated by a single geometrically described element.
dc.description.urihttp://libproxy1.nus.edu.sg/login?url=http://dx.doi.org/10.2140/agt.2011.11.887
dc.sourceScopus
dc.typeArticle
dc.contributor.departmentMATHEMATICS
dc.description.doi10.2140/agt.2011.11.887
dc.description.sourcetitleAlgebraic and Geometric Topology
dc.description.volume11
dc.description.issue2
dc.description.page887-908
dc.identifier.isiut000289847900009
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