Embedding Heegaard Decompositions
نویسندگان
چکیده
A smooth embedding of a closed $3$-manifold $M$ in $\mathbb{R}^4$ may generically be composed with projection to the fourth coordinate determine Morse function on and hence Heegaard splitting $M=X\cup_\Sigma Y$. However, starting splitting, we find an obstruction coming from geometry curve complex $C(\Sigma)$ realizing corresponding $M\hookrightarrow \mathbb{R}^4$.
منابع مشابه
Comparing Open Book and Heegaard Decompositions of 3-manifolds
We study the maximal value of the Euler characteristic of the pages of all open book decompositions of closed orientable 3-manifolds. In particular, we describe some examples where the minimal genus Heegaard splittings of such 3-manifolds give rise to open book decompositions and other examples where the simplest open book decomposition has larger maximal Euler characteristic of pages than the ...
متن کاملMetric Embedding via Shortest Path Decompositions
We study the problem of embedding weighted graphs of pathwidth k into `p spaces. Our main result is an O(kmin{/p,/2})-distortion embedding. For p = 1, this is a super-exponential improvement over the best previous bound of Lee and Sidiropoulos. Our distortion bound is asymptotically tight for any fixed p > 1. Our result is obtained via a novel embedding technique that is based on low depth deco...
متن کاملDistances of Heegaard splittings
J Hempel [Topology, 2001] showed that the set of distances of the Heegaard splittings (S,V, h(V)) is unbounded, as long as the stable and unstable laminations of h avoid the closure of V ⊂ PML(S). Here h is a pseudo-Anosov homeomorphism of a surface S while V is the set of isotopy classes of simple closed curves in S bounding essential disks in a fixed handlebody. With the same hypothesis we sh...
متن کاملInvolutive Heegaard Floer Homology
Using the conjugation symmetry on Heegaard Floer complexes, we define a three-manifold invariant called involutive Heegaard Floer homology, which is meant to correspond to Z4-equivariant Seiberg-Witten Floer homology. Further, we obtain two new invariants of homology cobordism, d and d̄, and two invariants of smooth knot concordance, V 0 and V 0. We also develop a formula for the involutive Heeg...
متن کاملStabilization of Heegaard Splittings
For each g ≥ 2 there is a 3-manifold with two genus g Heegaard splittings that require g stabilizations to become equivalent. Previously known examples required at most one stabilization. Control of families of Heegaard surfaces is obtained through a deformation to
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: New Zealand journal of mathematics
سال: 2021
ISSN: ['1171-6096', '1179-4984']
DOI: https://doi.org/10.53733/189