arXiv research

Agol's announcement proved a full classification of certain Kleinian groups.

This paper connects veering triangulations to pseudo-Anosov flows on 3-manifolds.

Study Agol cycles for pseudo-Anosov 3-braids.

Study Agol cycles in pseudo-Anosov 3-braids.

Agol proved that hyperbolic cubulated groups are virtually special. The aim of these notes is to make the proof accessible to a wider audience; we retain the underlying ideas and constructions of Agol, but substantially change or add to many parts of the argument to give a more transparent and detailed account.

Study Agol cycles on 2-punctured torus and 5-punctured sphere, finding new dilatation formula.

Buser's inequality gives an upper bound on the first non-zero eigenvalue of the Laplacian of a closed manifold M in terms of the Cheeger constant h(M). Agol later gave a quantitative improvement of Buser's inequality. Agol's result is less transparent since it is given implicitly by a set of equations, one of which is …

Generalized Agol's theorem to 3-manifold groups.

Answering a question asked by Agol and Wise, we show that a desired stronger form of Wise's malnormal special quotient theorem does not hold. The counterexamples are generalizations of triangle groups, built using the Ramanujan graphs constructed by Lubotzky--Phillips--Sarnak.

In 2007 Agol showed that if N is an aspherical compact 3-manifold with empty or toroidal boundary such that its fundamental group is virtually RFRS, then $N$ is virtually fibered. We give a largely self-contained proof of Agol's theorem using complexities of sutured manifolds.

Investor emotions predict earnings announcements, but excitement lowers returns.

Agol recently introduced the concept of a veering taut triangulation, which is a taut triangulation with some extra combinatorial structure. We define the weaker notion of a "veering triangulation" and use it to show that all veering triangulations admit strict angle structures. We also answer a question of Agol, givin…

We give a general lower bound for the normal Gromov norm of genuine laminations in terms of the topology of the complementary regions. In the special case of 3-manifolds, this yields a generalization of Agol's inequality from incompressible surfaces to tight laminations. In particular, the inequality excludes the exist…

This study examines how earnings announcements affect option volatility and pricing.

The study classifies policy announcements' impact on stock market volatility.

Predicts stock price changes based on clinical trial announcements.

This an announcement for the generalized asymptotic expansion of Tian-Yau-Zeldtich.

Media tone around earnings announcements predicts stock returns.

The paper embeds non-arithmetic hyperbolic manifolds into higher-dimensional spaces.

Recently, Ian Agol introduced a class of "veering" ideal triangulations for mapping tori of pseudo-Anosov homeomorphisms of surfaces punctured along the singular points. These triangulations have very special combinatorial properties, and Agol asked if these are "geometric", i.e. realised in the complete hyperbolic met…

The above title is the same, but with "semisimple" instead of "simple," as that of a notice by N. Kowalsky. There, she announced many theorems on the subject of actions of simple Lie groups preserving a Lorentz structure. Unfortunately, she published proofs for essentially only half of the announced results before her …

This study analyzes how the Indian stock market reacts to budget announcements using fractal methods.

We study an option pricing framework that accounts for the price impact of an earnings announcement (EA), and analyze the behavior of the implied volatility surface prior to the event. On the announcement date, we incorporate a random jump to the stock price to represent the shock due to earnings. We consider different…

We summarize properties of 3-manifold groups, with a particular focus on the consequences of the recent results of Ian Agol, Jeremy Kahn, Vladimir Markovic and Dani Wise.

This paper introduces a non-parametric framework to statistically examine how news events, such as company or macroeconomic announcements, contribute to the pre- and post-event jump dynamics of stock prices under the intraday seasonality of the news and jumps. We demonstrate our framework, which has several advantages …

We present a Hawkes model approach to foreign exchange market in which the high frequency price dynamics is affected by a self exciting mechanism and an exogenous component, generated by the pre-announced arrival of macroeconomic news. By focusing on time windows around the news announcement, we find that the model is …

This thesis identifies share buybacks and predicts their impact on stock performance.

Considered an important macroeconomic indicator, the Purchasing Managers' Index (PMI) on Manufacturing generally assumes that PMI announcements will produce an impact on stock markets. International experience suggests that stock markets react to negative PMI news. In this research, we empirically investigate the stock…

We find a larger class of virtually fibred classic Montesinos links of type $\widetilde{SL_2}$, extending a result of Agol, Boyer and Zhang.

Study predicts stock price direction on earnings announcement days using multi-modal deep learning.

Study finds financial YouTube channel 3PROTV predicts stock market performance and sentiment changes.

Using recent results of Agol, Przytycki-Wise and Wise we show that twisted Alexander polynomials detect the Thurston norm of any irreducible 3-manifold which is not a closed graph manifold.

New framework predicts earnings announcements using press release content, surpassing earnings surprises.

The attack intensity of distributed denial of service (DDoS) attacks is increasing every year. Botnets based on internet of things (IOT) devices are now being used to conduct DDoS attacks. The estimation of direct and indirect economic damages caused by these attacks is a complex problem. One of the indirect damage of …

We construct a locally hyperbolic 3-manifold $M_\infty$ such that $π_ 1(M_\infty)$ has no divisible subgroup. We then show that $M_\infty$ is not homeomorphic to any complete hyperbolic manifold. This answers a question of Agol [DHM06,Mar07].

We prove that the three-sphere recognition problem lies in the complexity class NP. Our work relies on Thompson's original proof that the problem is decidable [Math. Res. Let., 1994], Casson's version of her algorithm, and recent results of Agol, Hass, and Thurston [ArXiv, 2002].

This paper quantifies the impact of Dow Jones Sustainability Index listing on stock returns.

Green bond leaks impact equity markets, altering investor reactions.

This is a research announcement of the theory of orbifold quantum cohomology.

Marden's Tameness Conjecture predicts that every hyperbolic 3-manifold with finitely generated fundamental group is homeomorphic to the interior of a compact 3-manifold. It was recently established by Agol and Calegari-Gabai. We will survey the history of work on this conjecture and discuss its many applications.

Study homomorphisms from groups to 3-manifold fundamental groups.

This paper is a follow-up to our joint paper with I. Agol, P. Storm and K. Whyte "Finiteness of arithmetic hyperbolic reflection groups". The main purpose is to investigate the effective side of the method developed there and its possible application to the problem of classification of arithmetic hyperbolic reflection …

We study the behavior of U.S. markets both before and after U.S. Federal Open Market Committee (FOMC) meetings, and show that the announcement of a U.S. Federal Reserve rate change causes a financial shock, where the dynamics after the announcement is described by an analogue of the Omori earthquake law. We quantify th…

The purpose of this note is to announce complete answers to the following questions. (1) For an essential simple loop on a 2-bridge sphere in a 2-bridge link complement, when is it null-homotopic in the link complement? (2) For two distinct essential simple loops on a 2-bridge sphere in a 2-bridge link complement, when…

Unique incompressible surface in fibered 3-manifolds.

The study reveals distinct patterns in retail investors' holding periods affecting stock returns.

This paper contains a purely topological theorem and a geometric application. The topological theorem states that if M is a simple closed orientable 3-manifold such that π_1(M) contains a genus g surface group and H_1(M;Z/2Z) has rank at least 4g-1 then M contains a closed incompressible surface of genus at most g. Thi…

This paper gives a complete proof of the result announced in the title.