# Higher-dimensional contact topology and quantum topology

> **NSF 01002526DB NSF RESEARCH & RELATED ACTIVIT** · University of California-Los Angeles (CA) · $300,000

## Abstract

Contact structures are central objects of study in modern geometry and topology.  They appear naturally as the boundary of space-time in mathematical physics, and as such, play an essential role in the mathematical study of three- and four-dimensional spaces and the knotting of DNA.  In dimension three, contact structures are comparatively well-understood due to dramatic advances in the previous decades.  The goal of this research project is to study the relationship of contact topology to quantum physics and to quantum invariants of knots and links and further develop the study of contact structures in higher dimensions, which is still in its infancy despite significant advances in recent years.  As part of this project, the Principal Investigator will also promote the training of future mathematicians.

This research project on higher-dimensional contact topology, Floer theory, and their interactions with quantum topology has two parts:  The first is to study the mathematics surrounding the recent discovery of the relationship between Hecke algebras --- essential ingredients in quantum knot invariants ---  and the higher-dimensional Heegaard Floer homology of the cotangent bundle of a surface.  One of the goals is to better understand the topological quantum field theory (TQFT) underlying this discovery, relate it to string topology, and define and analyze the 3- and 4-manifold invariants corresponding to this theory.  The second is to continue the systematic study of con

## Key facts

- **NSF award ID:** 2505876
- **Awardee organization:** University of California-Los Angeles (CA)
- **SAM.gov UEI:** RN64EPNH8JC6
- **PI:** Ko Honda
- **Primary program:** 01002526DB NSF RESEARCH & RELATED ACTIVIT
- **All programs:** —
- **Estimated total:** $300,000
- **Funds obligated:** $300,000
- **Transaction type:** Standard Grant
- **Period:** 07/01/2025 → 06/30/2028

## Primary source

NSF Award Search: https://www.nsf.gov/awardsearch/showAward?AWD_ID=2505876

## Citation

> US National Science Foundation, Award 2505876, Higher-dimensional contact topology and quantum topology. Retrieved via AI Analytics 2026-06-08 from https://api.ai-analytics.org/grant/nsf/2505876. Licensed CC0.

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