Related papers: Essential loops in taut ideal triangulations

A degree-regular triangulation is one in which each vertex has identical degree. Our main result is that any such triangulation of a (possibly non-compact) surface $S$ is geometric, that is, it is combinatorially equivalent to a geodesic…

We show that fundamental groups of compact, orientable, irreducible 3-manifolds with toroidal boundary are Grothendieck rigid.

Work of Kalelkar, Schleimer, and Segerman shows that, with some exceptions, the set of essential ideal triangulations of an orientable cusped hyperbolic 3-manifold is connected via 2-3 and 3-2 moves. It is natural to ask if the subgraph…

Let M be an oriented compact 3-manifold and let T be a (loose) triangulation of M, with ideal vertices at the components of the boundary of M and possibly internal vertices. We show that any spin structure s on M can be encoded by extra…

For a given cusped 3-manifold $M$ admitting an ideal triangulation, we describe a method to rigorously prove that either $M$ or a filling of $M$ admits a complete hyperbolic structure via verified computer calculations. Central to our…

This paper initiates the study of circular orderability of $3$-manifold groups, motivated by the L-space conjecture. We show that a compact, connected, $\mathbb{P}^2$-irreducible $3$-manifold has a circularly orderable fundamental group if…

We prove that the fundamental group of any Seifert 3-manifold is conjugacy separable. That is, conjugates may be distinguished in finite quotients or, equivalently, conjugacy classes are closed in the pro-finite topology.

We apply the effective field theory approach to the three-nucleon system. In particular, we consider S=1/2 neutron-deuteron scattering and the triton. We show that in this channel a unique nonperturbative renormalization takes place which…

This paper is the third in a sequence establishing a dictionary between the combinatorics of veering triangulations equipped with appropriate filling slopes, and the dynamics of pseudo-Anosov flows (without perfect fits) on closed…

A Delta-groupoid is an algebraic structure which axiomatizes the combinatorics of a truncated tetrahedron. By considering two simplest examples coming from knot theory, we illustrate how can one associate a Delta-groupoid to an ideal…

We prove that for a torus homeomorphism isotopic to the identity and with a lift whose rotation set is an interval, either every rational point in the rotation set is realized by a periodic orbit, or there exists an annular, essential,…

In this paper it is proven that if the group of covering translations of the covering space of a compact, connected, $P^2$-irreducible 3-manifold corresponding to a non-trivial, finitely-generated subgroup of its fundamental group is…

A well-known result of Walsh states that if $\mathcal T^*$ is an ideal triangulation of an atoroidal, acylindrical, irreducible, compact 3-manifold with torus boundary components, then every properly embedded, two-sided, incompressible…

We show that the hyperbolic structure on a closed, orientable, hyperbolic 3-manifold can be constructed from a solution to the hyperbolic gluing equations using any triangulation with essential edges. The key ingredients in the proof are…

We construct a combinatorial invariant of 3-orbifolds with singular set a link that generalizes the Turaev torsion invariant of 3-manifolds. We give several gluing formulas from which we derive two consequences. The first is an…

Turaev Viro invariants are amongst the most powerful tools to distinguish 3-manifolds: They are implemented in mathematical software, and allow practical computations. The invariants can be computed purely combinatorially by enumerating…

A notion of fundamental group of spectral triples has been introduced. The notion uses a noncommutative analogue of unramified coverings. It was shown that in commutative case this fundamental group is a profinite completion of fundamental…

Any two triangulations of a closed surface with the same number of vertices can be transformed into each other by a sequence of regular flips, provided the number of vertices exceeds a number N depending on the surface. Examples show that…

In this note we show that many subgroups of mapping class groups of infinite-type surfaces without boundary have trivial centers, including all normal subgroups. Using similar techniques, we show that every nontrivial normal subgroup of a…

We introduce an analogue of the Novikov Conjecture on higher signatures in the context of the algebraic geometry of (nonsingular) complex projective varieties. This conjecture asserts that certain "higher Todd genera" are birational…