The Torelli group of a genus g$g$ oriented surface Σg$Sigma _g$ is the subgroup Ig$mathcal {I}_g$ of the mapping class group Mod(Σg)${rm Mod}(Sigma _g)$ consisting of all mapping classes that act trivially on H1(Σg,Z)${rm H}_1(Sigma _g, mathbb {Z})$. The qu...
Witten genus就会出现. 构造因子化代数用的主要工具就是他和Owen搞的那个微扰重整化machinery.话说我想知...
Ann. 215 (1975), 173--193. ), detects the undecided$\\mathbf{Z}_2$ factor in $H_2(\\mathbf{M}_3;\\mathbf{Z})$.doi:10.48550/arXiv.1311.5705Wolfgang PitschMathematicsW. Pitsch, The 2-torsion in the second homology of the genus 3 mapping class group, preprint, arXiv:1311.5705....
We used this assumption to control the “ index” on ECH, which in turn bounds the genus of holomorphic curves and allows us to find the genus zero curve we want. To remove this assumption, while continuing using our proof strategy, one would need to do more research on the index to se...
closed incompressible surface in M has genus at least g. We shall denote the Heegaard genus of a 3-manifold Q by Hg(Q). Theorem 5.8. Suppose M is a closed, simple 3-manifold containing a separating connected closed incompressible surface of some genus g, that Hg(M) ≥ g +4, and tha...
We obtain a surface of genus 2 with two components of boundary: ∂1S(1,1) and ∂2S(1,2). Attaching the copies D1(1),D2(1) of the discs D1,D2 to these components gives a closed surface N of genus 2. One more copy of this surface will be denoted by K (see the bottom ...
Yet, this simple, easy to compute number can already distinguish the different types of closed, oriented surfaces: for the sphere we have χ=2, the torus χ=0, and in general for any surface Mg of genus g χ(Mg)=2−2g The Euler characteristic also tells us something about the ...
Hamiltonian handleslides for Heegaard Floer homologyA $g$-tuple of disjoint, linearly independent circles in a Riemann surface of genus $g$ determines a `Heegaard torus' in its $g$-fold symmetric product. Changing the circles by a handleslide produces a new torus. It is proved that, for ...
Fig. 5: Bootstraps for coronavirus consensus genus topology. The coronavirus genus topology is(((A,B),G),D)with high ensemble confidence (Fig.4). Using the default Muscle5 MSA (none.0), this topology was reported by four of the six tree estimation methods with bootstraps as shown in...
Shewanella is a genus of marine and freshwater gram-negative Gammaproteobacteria within the monogeneric family Shewanellaceae Ivanova et al., 2004. While members of Shewanella have been recognized since 1931 (e.g. Achromobacter putrefaciens Derby and Hammer 1931 now Shewanella putrefaciens), the genus...