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Prime component-preservingly amphicheiral link with odd minimal crossing number
component-preservingly amphicheiral link minimal crossing number Tait's conjecture
2012/3/1
For every odd integer $c\ge 21$, we raise an example of a prime component-preservingly amphicheiral link with minimal crossing number $c$.
On visualization of the linearity problem for mapping class groups of surfaces
visualization linearity problem mapping class groups surfaces
2012/3/1
We derive two types of linearity conditions for mapping class groups of orientable surfaces; one for once-punctured surface, and the other for closed surface, respectively. For the once-punctured case...
$Top(X)$ within $\px$ ]{When lattices meet topology: $Top(X)$ within $\px$.}
$Top(X)$ within $\px$ lattices meet topology
2012/2/29
For a non-empty set $X$, the collection $Top(X)$ of all topologies on $X$ sits inside the Boolean lattice $\PP(\PP(X))$ (when ordered by set-theoretic inclusion) which in turn can be naturally identif...
Finiteness of nonzero degree maps between three-manifolds
Finiteness of nonzero degree maps three-manifolds Geometric Topology
2011/9/22
Abstract: In this paper, we prove that every orientable closed 3-manifold dominates at most finitely many homeomorphically distinct irreducible non-geometric 3-manifolds. Moreover, for any integer $d>...
Abstract: Heegaard Floer theory is a kind of topological quantum field theory, assigning graded groups to closed, connected, oriented 3-manifolds and group homomorphisms to smooth, oriented 4-dimensio...
Systole et rayon maximal des variétés hyperboliques non compactes
Hyperbolic Manifolds Cusps Systole and Inradius
2011/9/23
Abstract: We bound two global invariants of cusped hyperbolic manifolds: the length of the shortest closed geodesic (the systole), and the radius of the biggest embedded ball (the inradius). We give a...
On the Associativity of Gluing
Morse theory negative gradient trajectories associativity of gluing compactified Moduli spaces manifold with faces
2011/9/22
Abstract: This paper studies the associativity of gluing of trajectories in Morse theory. We show that the associativity of gluing follows from of the existence of compatible manifold with face struct...
On the Kauffman-Vogel and the Murakami-Ohtsuki-Yamada Graph Polynomials
Kauffman polynomial HOMFLY-PT polynomia Geometric Topology
2011/9/21
Abstract: This paper consists of three parts. First, we generalize the Jaeger Formula to express the Kauffman-Vogel graph polynomial as a state sum of the Murakami-Ohtsuki-Yamada graph polynomial.
Covolumes of nonuniform lattices in PU(n, 1)
Covolumes of nonuniform lattices Geometric Topology
2011/9/21
Abstract: This paper studies the covolumes of nonuniform arithmetic lattices in PU(n, 1). We determine the smallest covolume nonuniform arithmetic lattices for each n, the number of minimal covolume l...
On overtwisted, right-veering open books
Contact surgery destabilizable diffeomorphisms Giroux’s correspondence open books overtwisted contact structures
2011/9/21
Abstract: We exhibit infinitely many overtwisted, right-veering, non-destabilizable open books, thus providing infinitely many counterexamples to a conjecture of Honda-Kazez-Matic. The page of all our...
Abstract: Let L \subset S^3 denote an alternating link and Sigma(L) its branched double-cover. We give a short proof of the fact that the fundamental group of Sigma(L) admits a left-ordering iff L is ...
A survey of quantum Teichmüller space and Kashaev algebra
shear coordinate quantum Teichmuller space Kashaev coordinates generalized Kashaev algebra
2011/9/20
Abstract: In this chapter, we survey the algebraic aspects of quantum Teichm\"uller space, generalized Kashaev algebra and a natural relationship between the two algebras.
Abstract: We show that the triangle with angles Pi/12, Pi/3 and 7*Pi/12 has the lattice property and compute this triangle's Veech group.
On L-spaces and left-orderable fundamental groups
left-orderable fundamental groups Geometric Topology
2011/9/20
Abstract: Examples suggest that there is a correspondence between L-spaces and 3-manifolds whose fundamental groups cannot be left-ordered. In this paper we establish the equivalence of these conditio...
Abstract: We show how to construct homology bases for certain CW complexes in terms of discrete Morse theory and cellular homology. We apply this technique to study certain subcomplexes of the half cu...