Journal of Topology最新文献

We study relative symplectic cobordisms between contact submanifolds, and in particular relative symplectic cobordisms to the empty set, that we call hats. While we make some observations in higher dimensions, we focus on the case of transverse knots in the standard 3-sphere, and hats in blow-ups of the (punctured) complex projective planes. We apply the construction to give constraints on the algebraic topology of fillings of double covers of the 3-sphere branched over certain transverse quasipositive knots.

We show that the Iwahori–Hecke algebras $�H_n$ of type $�A_{�n�-�1�}$ satisfy homological stability, where homology is interpreted as an appropriate Tor group. Our result precisely recovers Nakaoka's homological stability result for the symmetric groups in the case that the defining parameter is equal to 1. We believe that this paper, and our joint work with Boyd on Temperley–Lieb algebras, are the first time that the techniques of homological stability have been applied to algebras that are not group algebras.

For any smooth connected linear algebraic group $�G$ over an algebraically closed field $�k$, we describe the Picard group of the universal moduli stack of principal $�G$-bundles over pointed smooth $�k$-projective curves.

We completely classify the possible divergence functions for right-angled Coxeter groups (RACGs). In particular, we show that the divergence of any such group is either polynomial, exponential, or infinite. We prove that a RACG is strongly thick of order $�k$ if and only if its divergence function is a polynomial of degree $��k�+�1�$. Moreover, we show that the exact divergence function of a RACG can easily be computed from its defining graph by an invariant we call the hypergraph index.

We classify the boundaries of hyperbolic groups that have enough quasiconvex codimension-1 surface subgroups with trivial or cyclic intersections.

We present the first examples of elements in the fundamental group of the space of Legendrian links in $��(�S^3�,�{\xi }_{\text{st}}�)�$ whose action on the Legendrian contact DGA is of infinite order. This allows us to construct the first families of Legendrian links that can be shown to admit infinitely many Lagrangian fillings by Floer-theoretic techniques. These new families include the first-known Legendrian links with infinitely many fillings that are not rainbow closures of positive braids, and the smallest Legendrian link with infinitely many fillings known to date. We discuss how to use our examples to construct other links with infinitely many fillings, and in particular give the first Floer-theoretic proof that Legendrian $��(�n�,�m�)�$ torus links have infinitely many Lagrangian fillings if $��n�⩾�3�,�m�⩾�6�$ or $��(�n�,�m�)�=�(�4�,�4�)�,�(�4�,�5�)�$. In addition, for any given higher genus, we construct a Weinstein 4-manifold homotopic to the 2-sphere whose wrapped Fukaya category can distinguish infinitely many exact closed Lagrangian surfaces of that genus in the same smooth isotopy class, but distinct Hamiltonian isotopy classes. A key technical ingredient behind our results is a new combinatorial formula for decomposable cob

We study the elliptic spectral sequence computing $��t�m�f_{\ast }��\left(�R�P^2�\right)��$ and $��t�m�f_{\ast }��(�R�P^2�\wedge �C�P^2�)��$. Specifically, we compute all differentials and resolve exotic extensions by 2, $�\eta$, and $�\nu$. For $��t�m�f_{\ast }��(�R�P^2�\wedge �C�P^2�)��$, we also compute the effect of the $�v_1$-self maps of $�$

We study the orientability of vector bundles with respect to a family of cohomology theories called $�\mathrm{EO}$-theories. The $�\mathrm{EO}$-theories are higher height analogues of real $�K$-theory $�\mathrm{KO}$. For each $�\mathrm{EO}$-theory, we prove that the direct sum of $�i$ copies of any vector bundle is $�\mathrm{EO}$-orientable for some specific integer $�i$. Using a splitting principal, we reduce to the case of the canonical line bundle over $�{\mathrm{CP}}^{\infty }$. Our method involves understanding the action of an order $�p$ subgroup of the Morava stabilizer group on the Morava $�E$-theory of $�{\mathrm{CP}}^{\infty }$. Our calculations have another application: We determine the homotopy type of the $�S^1$-Tate spectrum associated to the trivial action of $�S^1$ on all $�\mathrm{EO}$

We prove that the polar degree of an arbitrarily singular projective hypersurface can be decomposed as a sum of non-negative numbers which quantify local vanishing cycles of two different types. This yields lower bounds for the polar degree of any singular projective hypersurface.

We show that curve complex distance is coarsely equal to electric distance in hyperbolic manifolds associated to Kleinian surface groups, up to errors that are polynomial in the complexity of the underlying surface. We then use this to control the quasi-isometry constants of maps between curve complexes induced by finite covers of surfaces. This makes effective previously known results, in the sense that the error terms are explicitly determined, and allows us to give several applications. In particular, we effectively relate the electric circumference of a fibered manifold to the curve complex translation length of its monodromy, and we give quantitative bounds on virtual specialness for cube complexes dual to curves on surfaces.