Knots, three-manifolds and instantons P. B. Kronheimer and T. S. Mrowka Low-dimensional topology is the study of manifolds and cell complexes in dimensions four and below. Input from geometry and analysis has been centra

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• Topology
• Mathematics
• Theoretical physics
• Algebraic topology
• Symplectic topology
• Homology theory
• Fellows of the Royal Society
• Floer homology
• Orbifold
• Manifold
• Low-dimensional topology
• Fundamental group

BRAID GROUPS, HECKE ALGEBRAS AND KNOT THEORY MARIA CHLOUVERAKI One of the greatest accomplishments in knot theory and low-dimensional topology is the pioneering construction of the Jones polynomial by V. F. R. Jones in 1

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Noah Snyder: Research Statement Quantum Algebra and Quantum Topology I work in an area at the intersection of representation theory, low-dimensional topology, higher category theory, and operator algebras which is often

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• Topology
• Mathematics
• Differential topology
• Surgery theory
• Maps of manifolds
• Capped grope
• Geometric topology
• Manifold
• Knot
• Low-dimensional topology
• Embedding
• Arf invariant

FROM CLAUSEN TO CARLITZ: LOW-DIMENSIONAL SPIN GROUPS AND IDENTITIES AMONG CHARACTER SUMS NICHOLAS M. KATZ Dedicated to Pierre Deligne, with the utmost admiration

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• Mathematics
• Mathematical analysis
• Algebra
• Ordinary differential equations
• Algebraic topology
• Sheaf
• Kloosterman sum
• Hypergeometric function
• Cohomology
• Lie groups
• Linear temporal logic
• Differential forms on a Riemann surface

EXOTIC OPEN 4-MANIFOLDS WHICH ARE NON-LEAVES ˜ COTON ´ AND PAUL A. SCHWEITZER, S.J. CARLOS MENINO We study the possibility of realizing exotic smooth structures on punctured simply connected 4-manifolds as leaves of a

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• Topology
• Geometric topology
• Manifolds
• Foliations
• Diffeomorphism
• Exotic R4
• 4-manifold
• 3-manifold
• Differentiable manifold
• Surface
• Low-dimensional topology
• Mazur manifold

Compositio Math–810 doi:S0010437X06002697 Jacobi identities in low-dimensional topology James Conant, Rob Schneiderman and Peter Teichner Abstract

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• Geometric topology
• Surgery theory
• Differential topology
• Algebraic topology
• Cobordism
• Kontsevich invariant
• Manifold
• Topological space
• Topology
• Monoid
• Capped grope
• Clasper

Higher-Order Intersections in Low-Dimensional Topology Jim Conant ∗ , Rob Schneiderman † , and Peter Teichner ‡ ∗ University of Tennessee,† Lehman College CUNY, and ‡ UC Berkeley and Max-Planck-Institut f¨

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• Surgery theory
• Knot invariants
• Differential topology
• 3-manifolds
• Geometric topology
• Link group
• Arf invariant
• Finite type invariant
• H-cobordism
• Manifold
• Link concordance
• Cobordism

Positivity and higher Teichmüller theory Anna Wienhard (Heidelberg University) Classical Teichmüller space describes the space of conformal structures on a given topological surface S. It plays an important role in sev

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• Geometry
• Space
• Riemann surfaces
• Geometric group theory
• Lie groups
• Moduli theory
• Differential geometry
• Teichmller space
• Teichmller
• SL2
• Differential geometry of surfaces
• Low-dimensional topology

Ultra-Low-Dimensional Embeddings for Doubling Metrics T-H. Hubert Chan∗ Anupam Gupta† Abstract

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• Metric geometry
• Lemmas
• Johnson–Lindenstrauss lemma
• Chernoff bound
• Embedding
• Metric space
• Algebraic number field
• Differential geometry of surfaces
• Mathematics
• Topology
• Geometry