arXiv subjects

Hugo Zhou

Publications and source records attributed to Hugo Zhou.

15 recordsLinked to original sources

arXiv2026

On L-space surgeries on two-bridge links

We classify the sets of $L$-space surgeries on all two-bridge links, providing the first examples of hyperbolic links for which such sets cannot be described as unions of finitely many rectangles in $\mathbb{Q}^2$. The proof relies on several different techniques, each of which is applicable in greater generality: we introduce a sufficient diagrammatic condition for links in $S^3$ to be persistently foliar, a property that implies that every non-trivial surgery on such links supports a coorientable taut foliation. We define a simplified model for the Heegaard Floer homology of rational surgeries on two-component $L$-space links, following the work of Manolescu-Ozsv\'ath, Liu, and Zemke, and use it to obtain obstructions to $L$-space surgeries. Finally, we use explicit computations of Turaev torsions to determine $L$-space surgeries in the case of generalised $L$-space links. Among the consequences of our results, we obtain an optimal uniform bound on the volume of any hyperbolic $L$-space that is surgery on a two-bridge link, together with a classification of all $L$-space satellite knots whose associated two-component pattern link is a two-bridge link.

math.GT↗

arXiv2026

Wall-OSS-0.5 Technical Report

Large-scale Vision-Language-Action (VLA) pretraining is increasingly adopted as the foundation for robot policies, yet the evidence for pretrained VLAs is almost invariably reported after task-specific fine-tuning. This leaves a foundational question unanswered: does VLA pretraining itself yield executable robot behavior, or does it merely furnish a better initialization for downstream policy learning? We present Wall-OSS-0.5, an open-source 4B VLA built upon a 3B VLM backbone augmented with action-generation components, designed so that pretrained robotic capability is directly measurable on physical hardware. The model is pretrained across more than 20 embodiments, processing over one million robot trajectories per epoch alongside a grounded multimodal corpus. We adopt a gradient-bridged co-training recipe in which three objectives play distinct and complementary roles: discrete action prediction routes strong VLM-native gradients into the backbone, multimodal prediction preserves grounded vision-language understanding, and continuous flow matching serves as the deployment-time action interface. Before task-specific fine-tuning, the pretrained checkpoint achieves non-trivial zero-shot real-robot behavior, completing several tasks, including a held-out deformable manipulation task, at high task progress on a 17-task suite. After fine-tuning, the same checkpoint serves as a stronger adaptation prior, reaching 60.5% average task progress on 15 real-robot tasks and outperforming \pi_0.5 by 17.5%. Multimodal evaluations further confirm that action training does not erode grounded vision-language competence: the model preserves broad vision-language ability while strengthening embodied grounding. Together, these results reposition VLA pretraining from an initialization strategy to a directly testable, already useful source of robot capability.

cs.RO↗

arXiv2026

The link surgery modules of 2-component L-space links

In our earlier work, we studied the link surgery modules of two component L-space links. Therein, we computed two of the four idempotents of such modules. In this article, we use Koszul duality to give an alternate account of this proof, and also to extend it to compute the entire link surgery modules of such links, modulo a technical result which will be proven in a subsequent paper.

math.GT↗

arXiv2025

Surgeries on knots and tight contact structures

For any knot $K$ in $S^3$ and any positive rational $r$, we show that smooth $(-r)$-surgery on $K$ always admits a tight contact structure. More specifically, the tightness is detected by the non-vanishing Heegaard Floer contact invariant.

math.GT↗

arXiv2025

Applications of the L-space satellite formula

We give a formula for the $\tau$-invariant of a satellite knot $P(K,n)$ when $P$ is an L-space satellite operator. Our formula holds for general L-space satellite operators $P$ when the companion $K$ satisfies $\epsilon(K)=1$. When $\epsilon(K)$ is $0$ or $-1$, we state a formula which requires some additional assumptions on $P$ or $n$. Our main tool is our algorithm which computes the knot Floer complex of satellite knots constructed using L-space satellite operators, which we developed in a previous paper. Our formula for $\tau$ recovers many existing formulas for the behavior of $\tau$ under satellite operators, including for cables. We apply our formula to questions about the slice genus of satellite knots, showing, e.g., that if $K$ is a knot with $\tau(K)=g_4(K)>0$, then satellites of $K$ by L-space satellite operators have the same property. Another application is a proof that L-space satellite operators satisfy a conjecture of Hedden and Pinz\'on-Caicedo: If $P$ is an L-space satellite operator which acts as a group homomorphism on the smooth concordance group, then $P$ is either the zero operator, the identity operator, or the orientation reversing operator.

math.GT↗

arXiv2025

Igniting VLMs toward the Embodied Space

While foundation models show remarkable progress in language and vision, existing vision-language models (VLMs) still have limited spatial and embodiment understanding. Transferring VLMs to embodied domains reveals fundamental mismatches between modalities, pretraining distributions, and training objectives, leaving action comprehension and generation as a central bottleneck on the path to AGI. We introduce WALL-OSS, an end-to-end embodied foundation model that leverages large-scale multimodal pretraining to achieve (1) embodiment-aware vision-language understanding, (2) strong language-action association, and (3) robust manipulation capability. Our approach employs a tightly coupled architecture and multi-strategies training curriculum that enables Unified Cross-Level CoT-seamlessly unifying instruction reasoning, subgoal decomposition, and fine-grained action synthesis within a single differentiable framework. Our results show that WALL-OSS attains high success on complex long-horizon manipulations, demonstrates strong instruction-following capabilities, complex understanding and reasoning, and outperforms strong baselines, thereby providing a reliable and scalable path from VLMs to embodied foundation models.

cs.RO↗

arXiv2024

L-space satellite operators and knot Floer homology

We consider satellite operators where the corresponding 2-component link is an L-space link. This family includes many commonly studied satellite operators, including cabling operators, the Whitehead operator, and a family of Mazur operators. We give a formula which computes the knot Floer complex of a satellite of $K$ in terms of the knot Floer complex of $K$. Our main tools are the Heegaard Floer Dehn surgery formulas and their refinements. A key step in our computation is a proof that 2-component L-space links have formal knot Floer complexes. We use this to show that the link Floer complexes of 2-component L-space links are determined by their multivariable Alexander polynomials. We implement our satellite formula in Python code, which we also make available.

math.GT↗

arXiv2024

Cubiquitous Lattices and Branched Covers bounding rational balls

Greene and Owens explore cubiquitous lattices as an obstruction to rational homology 3-spheres bounding rational homology 4-balls. The purpose of this article is to better understand which sublattices of $\mathbb{Z}^n$ are cubiquitous with the aim of effectively using their cubiquity obstruction. We develop a geometric obstruction (called the Wu obstruction) to cubiquity and use it as tool to completely classify which sublattices with orthogonal bases are cubiquitous. We then apply this result the double branched covers of alternating connected sums of torus links. Finally, we explore how the Wu obstruction can be used in conjunction with contractions to obstruct the cubiquity of infinite families of lattices.

math.GT↗

arXiv2024

Negative contact surgery on Legendrian non-simple knots

We prove that for any pair of Legendrian representatives of the Chekanov-Eliashberg twist knots with different LOSS invariants, any negative rational contact $r$-surgery with $r\neq -1$ always gives rise to different contact 3-manifolds distinguished by their contact invariants. This gives the first examples of pairs of Legendrian knots with the same classical invariants but distinct contact $r$-surgeries for all negative rational number $r$. We also generalize the statement from the twist knots to a certain families of two-bridge knots.

math.GT↗

arXiv2024

Evolving Agents: Interactive Simulation of Dynamic and Diverse Human Personalities

Human-like Agents with diverse and dynamic personalities could serve as an essential design probe in the process of user-centered design, thereby enabling designers to enhance the user experience of interactive applications. In this article, we introduce Evolving Agents, a novel agent architecture that consists of two systems: Personality and Behavior. The Personality system includes Cognition, Emotion, and Character Growth modules. The Behavior system comprises two modules: Planning and Action. We also build a simulation platform that enables agents to interact with the environment and other agents. Evolving Agents can simulate the human personality evolution process. Compared to its initial state, agents' personality and behavior patterns undergo believable development after several days of simulation. Agents reflect on their behavior to reason and develop new personality traits. These traits, in turn, generate new behavior patterns, forming a feedback loop-like personality evolution. Our experiment utilized a simulation platform with ten agents for evaluation. During the assessment, these agents experienced believable and inspirational personality evolution. Through ablation and control experiments, we demonstrated the effectiveness of agent personality evolution, and all of our agent architecture modules contribute to creating believable human-like agents with diverse and dynamic personalities. We also demonstrated through workshops how Evolving Agents could inspire designers.

cs.HC↗

arXiv2023

On homology concordance in contractible manifolds and two bridge links

Let $\widehat{\mathcal{C}}_\mathbb{Z}$ be the group consists of manifold-knot pairs $(Y,K)$ modulo homology concordance, where $Y$ is an integer homology sphere bounding an integer homology ball, and let $\mathcal{C}_\mathbb{Z}$ be the subgroup consisting of pairs $(S^3,K)$. Dai-Hom-Stoffregen-Truong show that the quotient group ${\widehat{\mathcal{C}}_\mathbb{Z}}/{\mathcal{C}_\mathbb{Z}}$ admits a $\mathbb{Z}^\infty$-summand. In this paper, we improve the result by showing that there exists a family $\{(Y,K_m)\}_{m>1 }$ generating the $\mathbb{Z}^\infty$-summand where $Y$ is the boundary of a smooth contractible $4$-manifold. In fact, we give a $\mathbb{Z}$-count of such families. The examples are constructed using a family of knots obtained by blowing down a component of a two-bridge link. They are studied in Jonathan Hales's thesis. Using the algorithm due to Ozsv\'{a}th, Szab\'{o} and Hales we give a classification of the knot Floer homology of a larger family of such knots, that might be of independent interest.

math.GT↗

arXiv2023

(1,1) almost L-space knots

We give a diagrammatic characterization of the $(1,1)$ knots in the three-sphere and lens spaces which admit large Dehn surgeries to manifolds with Heegaard Floer homology of next-to-minimal rank. This is inspired by a corresponding result for $(1,1)$ knots which admit large Dehn surgeries to manifolds with Heegaard Floer homology of minimal rank due to Greene-Lewallen-Vafaee.

math.GT↗

arXiv2023

PL-genus of surfaces in homology balls

We consider manifold-knot pairs $(Y,K)$ where $Y$ is a homology sphere that bounds a homology ball. We show that the minimum genus of a PL surface $\Sigma$ in a homology ball $X$ such that $\partial (X, \Sigma) = (Y, K)$ can be arbitrarily large. Equivalently, the minimum genus of a surface cobordism in a homology cobordism from $(Y, K)$ to any knot in $S^3$ can be arbitrarily large. The proof relies on Heegaard Floer homology.

math.GT↗

arXiv2022

A filtered mapping cone formula for cables of the knot meridian

We construct a filtered mapping cone formula that computes the knot Floer complex of the $(n,1)$--cable of the knot meridian in any rational surgery, generalizing Truong's result about the $(n,1)$--cable of the knot meridian in large surgery and Hedden-Levine's filtered mapping cone formula. As an application, we show that there exist knots in integer homology spheres with arbitrary $\varphi_{i,j}$ values for any $i>j\geq 0$, where $\varphi_{i,j}$ are the concordance homomorphisms defined by Dai-Hom-Stoffregen-Truong.

math.GT↗

arXiv2020

Homology concordance and an infinite rank free subgroup

Two knots are homology concordant if they are smoothly concordant in a homology cobordism. The group $\hat{\mathcal{C}}_{\mathbb{Z}}$ (resp. $\mathcal{C}_{\mathbb{Z}}$) was previously defined as the set of knots in homology spheres that bounds homology balls (resp. in $S^3$), modulo homology concordance. We prove $\hat{\mathcal{C}}_{\mathbb{Z}} / \mathcal{C}_{\mathbb{Z}}$ contains a $\mathbb{Z}^{\infty}$ subgroup. We construct our family of examples by applying the filtered mapping cone formula to $L$--space knots, and prove linear independence with the help of the connected knot complex.

math.GT↗