منابع مشابه
Alternate Heegaard genus bounds distance
Suppose M is a compact orientable irreducible 3-manifold with Heegaard splitting surfaces P and Q. Then either Q is isotopic to a possibly stabilized copy of P or the distance d(P) ≤ 2genus(Q). More generally, if P and Q are bicompressible but weakly incompressible connected closed separating surfaces in M then either • P and Q can be well-separated or • P and Q are isotopic or
متن کاملQuantum invariants provide sharp Heegaard genus bounds
Using Seifert fibered three-manifold examples of Boileau and Zieschang, we demonstrate that the Reshetikhin-Turaev quantum invariants may be used to provide a sharp lower bound on the Heegaard genus which is strictly larger than the rank of the fundamental group.
متن کاملQuantum invariants can provide sharp Heegaard genus bounds
Using Seifert fibered three-manifold examples of Boileau and Zieschang, we demonstrate that the Reshetikhin-Turaev quantum invariants may be used to provide a sharp lower bound on the Heegaard genus which is strictly larger than the rank of the fundamental group.
متن کاملHeegaard Floer correction terms and rational genus bounds
Given an element in the first homology of a rational homology 3– sphere Y , one can consider the minimal rational genus of all knots in this homology class. This defines a function Θ on H1(Y ;Z), which was introduced by Turaev as an analogue of Thurston norm. We will give a lower bound for this function using the correction terms in Heegaard Floer homology. As a corollary, we show that Floer si...
متن کاملThe Asymptotic Behaviour of Heegaard Genus
Heegaard splittings have recently been shown to be related to a number of important conjectures in 3-manifold theory: the virtually Haken conjecture, the positive virtual b1 conjecture and the virtually fibred conjecture [3]. Of particular importance is the rate at which the Heegaard genus of finite-sheeted covering spaces grows as a function of their degree. This was encoded in the following d...
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ژورنال
عنوان ژورنال: Geometry & Topology
سال: 2006
ISSN: 1364-0380,1465-3060
DOI: 10.2140/gt.2006.10.593