arXiv research

Identifies a mod-$p$ triple cup product for rational homology 3-spheres with specific first homology.

Study TMF-valued TQFT for closed 3-manifolds using torsion linking pairings.

Paper connects homologically fibered links to solutions of equations.

Paper proves triple linking form vanishes under specific conditions.

The paper introduces a new linking form for 3-manifolds in $S^4$.

Classifies modules of surface-knots in terms of their properties.

Matveev introduced Borromean surgery on 3-manifolds, and proved that the equivalence relation on closed, oriented 3-manifolds generated by Borromean surgeries is characterized by the first homology group and the torsion linking pairing. Massuyeau generalized this result to closed, spin 3-manifolds, and the second autho…

We present a classification theorem for closed smooth spin 2-connected 7-manifolds M. This builds on the almost-smooth classification from the first author's thesis. The main additional ingredient is an extension of the Eells-Kuiper invariant for any closed spin 7-manifold, regardless of whether the spin characteristic…

The Milnor degree of a 3-manifold is an invariant that records the maximum simplicity, in terms of higher order linking, of any link in the 3-sphere that can be surgered to give the manifold. This invariant is investigated in the context of torsion linking forms, nilpotent quotients of the fundamental group, Massey pro…

We discuss the ribbon-move for 2-knots, which is a local move. Let $K$ and $K'$ be 2-knots. Then we have: Suppose that $K$ and $K'$ are ribbon-move equivalent. (1) Let ${\mathrm {Tor}} H_1(\widetilde X_K; {\Z})$ (resp. ${\mathrm {Tor}} H_1(\widetilde X_{K'}; {\Z})$) be the $\Z$-torsion submodule of the Alexander module…

This is a collection of notes on embedding problems for 3-manifolds. The main question explored is `which 3-manifolds embed smoothly in the 4-sphere?' The terrain of exploration is the Burton/Martelli/Matveev/Petronio census of triangulated prime closed 3-manifolds built from 11 or less tetrahedra. There are 13766 mani…

Proves Poincaré duality for Hopf algebroids with bijective antipode.

New proof of chain duality for simplicial complexes.

Introduces Kähler duality between domains in complex space.

Research on dualities in geometric stereotypes.

Duality restored in gauge theory, gravity, and string theory models.

Unified proof of four Bavard dualities and new results on quasimorphisms.

Verma Howe duality connects tensor products of Verma modules to LKB representations.

Cohomological and homological spectral sequences are shown to be isomorphic.

The paper proves T-duality and Hori formulae for winding loop spaces.

Equivariant T-duality connects bundles with twists.

We give the definition of a duality that is applicable to arbitrary $k$-forms. The operator that defines the duality depends on a fixed form $Ω$. Our definition extends in a very natural way the Hodge duality of $n$-forms in $2n$ dimensional spaces and the generalized duality of two-forms. We discuss the properties of …

The paper establishes T-duality for 2D σ-models with H-flux.

QP perspective on Poisson-Lie T-duality topology changes.

Unified framework for T-duality in both trivial and non-trivial topologies.

Geometric duality connects graph isomorphism and knot equivalence.

Koszul duality for manifold modules proven.

This dissertation explores T-duality between hyperkähler structures and branes on algebraic integrable systems.

Maps self-duality in little disks operad to framed manifolds.

We study generalized complex structures and $T$-duality (in the sense of Bouwknegt, Evslin, Hannabuss and Mathai) on Lie algebras and construct the corresponding Cavalcanti and Gualtieri map. Such a construction is called "Infinitesimal $T$-duality". As an application we deal with the problem of finding symplectic stru…

New spherical T-duality for higher degree forms in fiber bundles.

The paper establishes a duality between non-compact and compact symmetric pairs.

We find the T-duality transformation rules for 2-dimensional (2,1) supersymmetric sigma-models in (2,1) superspace. Our results clarify certain aspects of the (2,1) sigma model geometry relevant to the discussion of T-duality. The complexified duality transformations we find are equivalent to the usual Buscher duality …

We study discrete group actions on coarse Poincare duality spaces, e.g. acyclic simplicial complexes which admit free cocompact group actions by Poincare duality groups. When G is an (n-1) dimensional duality group and X is a coarse Poincare duality space of formal dimension n, then a free simplicial action of G on X d…

The paper shows plentiful non-homotopy finite Poincaré duality spaces.

Study S-duality and supersymmetry on curved manifolds using localization.

We study the convex duality method for robust utility maximization in the presence of a random endowment. When the underlying price process is a locally bounded semimartingale, we show that the fundamental duality relation holds true for a wide class of utility functions on the whole real line and unbounded random endo…

In this paper, we show that if G is a finite p-group (p prime) acting by automorphisms on a $δ$-hyperbolic Poincare Duality group, then the fixed subgroup is a Poincare Duality group over Z/p. We also provide examples to show that the fixed subgroup might not even be a Duality group over Z.

Unified treatment of reinforcement learning via convex duality.

Dualities in physics help in machine learning tasks.

New approach to T-duality using Courant algebroids.

Proves a theorem for 3D Poincaré duality pairs.

New Langlands duality conjectures for 3-manifold skein modules.

Explains partial duality for ribbon graphs in simple terms.

The paper proves a generalized Lefschetz duality for a specific type of manifold.

Extends T-duality to more general fibrations, proving isomorphic cohomology and algebroids.

The paper studies Fox pairings of Poincaré duality groups using group cohomology.

Proves Verdier duality for sheaves on stratified spaces.