arXiv research

Study negative definite spin fillings of knot covers.

Proves Gromov's conjecture on total mean curvature using surgery and positive mass theorems.

Study shows certain spin manifolds can't meet DEC condition.

Researchers prove an inequality linking spin manifold fill-ins to hyperspherical radius.

New rigidity theorems for spin fill-ins with non-negative scalar curvature.

Proves upper bound on filling radius for manifolds with positive scalar curvature.

Upper bound for total mean curvature of spin fill-ins is proven.

This note fills a hole in the author's previous paper ``Ricci-Flat Holonomy: a Classification'', by dealing with irreducible holonomy algebras that are subalgebras or real forms of $\mbb{C} \oplus \mf{spin}(10,\mbb{C})$. These all turn out to be of Ricci-type.

In this paper we study ${\rm Spin}(7)$-instantons on asymptotically conical ${\rm Spin}(7)$-orbifolds (and manifolds) obtained by filling in certain squashed $3$-Sasakian $7$-manifolds. We construct a $1$-parameter family of explicit ${\rm Spin}(7)$-instantons. Taking the parameter to infinity, the family (a) bubbles o…

Given a spin$^c$ rational homology sphere $(Y,\mathfrak{s})$ with $\mathfrak{s}$ self-conjugate and for which the reduced monopole Floer homology $\mathit{HM}_{\bullet}(Y,\mathfrak{s})$ has rank one, we provide obstructions to the intersection forms of its Stein fillings which are not negative definite. The proof of th…

Study cyclic group actions on spin 4-manifolds with boundary using Seiberg-Witten theory.

We define an invariant for compact spin manifolds $X$ of dimension $4k$ equipped with a metric $h$ of positive Yamabe invariant on its boundary. The vanishing of this invariant is a necessary condition for the conformal class of $h$ to be the conformal infinity of a conformally compact Einstein metric on $X$.

The paper calculates involutive Heegaard Floer homology for specific 3-manifolds.

Assume that we are given a closed chord-generic Legendrian submanifold $Λ\subset P \times \mathbb R$ of the contactisation of a Liouville manifold, where $Λ$ moreover admits an exact Lagrangian filling $L_Λ \subset \mathbb R \times P \times \mathbb R$ inside the symplectisation. Under the further assumptions that this …

Upper estimate of Dirac eigenvalue linked to hyperspherical radius.

Proves positive mass theorems for specific ALF and ALG manifolds.

Study of conformally compact metrics and Lovelock tensors in even dimensions.

According to Giroux, contact manifolds can be described as open books whose pages are Stein manifolds. For 5-dimensional contact manifolds the pages are Stein surfaces, which permit a description via Kirby diagrams. We introduce handle moves on such diagrams that do not change the corresponding contact manifold. As an …

We introduce a refinement of the Ozsvath-Szabo complex associated to a balanced sutured manifold $(X,τ)$ by Juhasz. An algebra $A_τ$ is associated to the boundary of a sutured manifold and a filtration of its generators by $H^2(X,\partial X;\Z)$ is defined. For a fixed Spin^c structure $s$ over the manifold $X'$, which…

Study Stein and Milnor fillings of links from surface singularities.

Proves upper bound on systolic ratio for circle fillings.

The paper constructs minimal coherent filling pairs on surfaces.

The paper classifies symplectic fillings of lens spaces and constructs cobordisms.

Computes A-polynomials of knots from Whitehead sister link fillings.

If a simple 3-manifold M admits a reducible and a toroidal Dehn filling, the distance between the filling slopes is known to be bounded by three. In this paper, we classify all manifolds which admit a reducible Dehn filling and a toroidal Dehn filling with distance 3.

We give three infinite families of examples of nonhyperbolic Dehn fillings on hyperbolic manifolds. A manifold in the first family admits two Dehn fillings of distance two apart, one of which is toroidal and annular, and the other is reducible and $\partial$-reducible. A manifold in the second family has boundary consi…

The compact exceptional Lie groups F4, E6, E7 and E8 have spinor groups as a subgroup as follows: E8 \supset Ss(16) \supset Spin(15) \supset Spin(14) \supset Spin(13), E7 \supset Spin(12) \supset Spin(11), E6 \supset Spin(10), F4 \supset Spin(9) \supset Spin(8) \supset Spin(7) \supset \cdot \cdot \cdot \supset Spin(1) …

Study $d$-invariants of L-space double branched covers of arborescent links.

The paper proves finiteness of cosmetic fillings on a specific type of 3-manifold.

Study generalizes Lebesgue curves to new space-filling and fractal sets.

We use Menke's JSJ-type decomposition theorem for symplectic fillings to reduce the classification of strong and exact symplectic fillings of virtually overtwisted torus bundles to the same problem for tight lens spaces. For virtually overtwisted structures on elliptic or parabolic torus bundles, this gives a complete …

Let M be a simple 3-manifold with a toral boundary component partial_0 M. If Dehn filling M along partial_0 M one way produces a toroidal manifold and Dehn filling M along partial_0 M another way produces a boundary-reducible manifold, then we show that the absolute value of the intersection number on partial_0 M of th…

If a hyperbolic 3-manifold M admits a reducible and a finite Dehn filling, the distance between the filling slopes is known to be 1. This has been proved recently by Boyer, Gordon and Zhang. The first example of a manifold with two such fillings was given by Boyer and Zhang. In this paper, we give examples of hyperboli…

Affirmative proof that rank 3 3-manifolds have filling links.

Study filling links in 3-manifolds to understand their topological properties.

New method fills cluster seeds with exact Lagrangian structures.

Study shows connectedness of Bowditch boundary persists in long Dehn fillings.

The paper explores spin^h structures and their obstructions.

This paper classifies and determines the length of the shortest filling pairs on a specific type of surface.

Positive braids have endless filling possibilities.

Let $M$ be an irreducible, compact, connected, orientable 3-manifold whose boundary is a torus. We show that if $M$ is hyperbolic, then it admits at most six finite/cyclic fillings of maximal distance 5. Further, the distance of a finite/cyclic filling to a cyclic filling is at most 2. If $M$ has a non-boundary-paralle…

Four-dimensional Einstein Dehn filling is impossible.

Study Stein fillings of planar contact 3-manifolds with relative trisection genus 2.

Study on Legendrian knots and their non-orientable Lagrangian fillings.

Study shows no large mean curvature fill-ins for nonnegative scalar curvature.

Study ${ m Spin}(7)$-dDT connections on manifolds with ${ m Spin}(7)$-structures.

We extend Thurston's metric to projective filling currents, embedding Teichmüller space into the larger space.

We give an algorithm which produces infinitely many pairwise exotic Stein fillings of the same contact 3-manifolds, applying positive allowable Lefschetz fibrations over the disk. As a corollary, for a large class of Stein fillings, we realize the topological invariants (i.e. fundamental group, homology group, homology…