Related papers: On Mixed Brieskorn Variety

The Khovanov homology of a link in $S^3$ and the Heegaard Floer homology of its branched double cover are related through a spectral sequence constructed by Ozsv\'ath and Szab\'o. This spectral sequence has topological applications but is…

Associated with each oriented link is the two variable Homflypt polynomial. The Morton-Franks-Williams (MFW) inequality gives rise to an expression for the Homflypt polynomial with MFW coefficient polynomials. These MFW coefficient…

Let $T$ be a torus and $B$ a compact $T-$manifold. Goresky, Kottwitz, and MacPherson show in \cite{GKM} that if $B$ is (what was subsequently called) a GKM manifold, then there exists a simple combinatorial description of the equivariant…

We show that if a fibered knot $K$ is expressed as a band--connected sum of $K_1, \ldots, K_n$, then each $K_i$ is fibered, and the genus of $K$ is greater than or equal to that of the connected sum of $K_1,\ldots,K_n$.

While the topological types of {normal} surface singularities with homology sphere link have been classified, forming a rich class, until recently little was known about the possible analytic structures. We proved in [Geom. Topol. 9(2005)…

We study the boundary of the Milnor fibre of real analytic singularities $f: (\bR^m,0) \to (\bR^k,0)$, $m\geq k$, with an isolated critical value and the Thom $a_f$-property. We define the vanishing zone for $f$ and we give necessary and…

We introduce a family of generalized Schr\"oder polynomials $S_\tau(q,t,a)$, indexed by triangular partitions $\tau$ and prove that $S_\tau(q,t,a)$ agrees with the Poincar\'e series of the triply graded Khovanov-Rozansky homology of the…

Given a planar curve singularity, we prove a conjecture of Oblomkov-Shende, relating the geometry of its Hilbert scheme of points to the HOMFLY polynomial of the associated algebraic link. More generally, we prove an extension of this…

We prove a new theorem of Tverberg type which confirms the conjecture of Blagojevic, Frick, and Ziegler about the existence of "balanced Tverberg partitions" (Conjecture 6.6 in, Tverberg plus constraints, Bull. London Math. Soc., 46 (2014)…

According to Medvedev and Scanlon, a polynomial $f(x)\in \bar{\mathbb Q}[x]$ of degree $d\geq 2$ is called disintegrated if it is not linearly conjugate to $x^d$ or $\pm C_d(x)$ (where $C_d(x)$ is the Chebyshev polynomial of degree $d$).…

Let $L$ be a link and $\Phi^{A}_{L}(q)$ its link invariant associated with the vector representation of the quantum (super)algebra $U_{q}(A)$. Let $F_{L}(r,s)$ be the Kauffman link invariant for $L$ associated with the…

We present a connection between the BFV-complex (abbreviation for Batalin-Fradkin-Vilkovisky complex) and the so-called strong homotopy Lie algebroid associated to a coisotropic submanifold of a Poisson manifold. We prove that the latter…

Let $f: X \to S$ be a unipotent degeneration of projective complex manifolds over a disc such that the reduction of the central fibre $Y=f^{-1}(0)$ is simple normal crossings, and let $X_\infty$ be the canonical nearby fibre. Building on…

Let $f\colon X\to Z$ be a Mori fibre space. McKernan conjectured that the singularities of $Z$ are bounded in terms of the singularities of $X$. Shokurov generalised this to pairs: let $(X,B)$ be a klt pair and $f\colon X\to Z$ a…

We calculate the Borel-Moore homology of affine Springer fibers of type $A$ associated to some regular semisimple nil elliptic elements. As a result, we obtain bigraded $\mf{S}_{n}$-modules whose bigraded Frobenius series are generalization…

We deduce an analogue of the Bogomolov conjecture for non-degenerate subvarieties in fibered products of families of elliptic curves from the author's recent theorem on equidistribution in families of abelian varieties. This generalizes…

Given a perfect field of exponential characteristic $e$ and a functor $f:\mathcal A\to\mathcal B$ between symmetric monoidal strict $V$-categories of correspondences satisfying the cancellation property such that the induced morphisms of…

We study the existence of Milnor fibration on a big enough sphere at infinity for a mixed polynomial $f: \bR^{2n} \to \bR^2$. By using strong non-degeneracy condition, we prove a counterpart of N\'emethi and Zaharia's fibration theorem. In…

By applying Seifert's algorithm to a special alternating diagram of a link L, one obtains a Seifert surface F of L. We show that the support of the sutured Floer homology of the sutured manifold complementary to F is affine isomorphic to…

We construct an action of a polynomial ring on the colored sl(2) link homology of Cooper-Krushkal, over which this homology is finitely generated. We define a new, related link homology which is finite dimensional, extends to tangles, and…