Journal of Topology最新文献

Let $�L$ be an exact Lagrangian submanifold of a cotangent bundle $��T^{\ast }�M�$, asymptotic to a Legendrian submanifold $��\Lambda �\subset �T^{\infty }�M�$. We study a locally constant sheaf of $�\infty$-categories on $�L$, called the sheaf of brane structures or $�{\mathrm{Brane}}_L$. Its fiber is the $�\infty$-category of spectra, and we construct a Hamiltonian invariant, fully faithful functor from $��\Gamma �(�L�,�{\mathrm{Brane}}_L�)�$ to the $�\infty$-category of sheaves of spectra on $�M$ with singular support in $�\Lambda$

Given a class of embeddings into a contact or a symplectic manifold, we give a sufficient condition, that we call isocontact or isosymplectic realization, for this class to satisfy a general $�h$-principle. The flexibility follows from the $�h$-principles for isocontact and isosymplectic embeddings, it provides a framework for classical results, and we give two new applications. Our main result is that embeddings transverse to a contact structure satisfy a full $�h$-principle in two cases: if the complement of the embedding is overtwisted, or when the intersection of the image of the formal derivative with the contact structure is strictly contained in a proper symplectic subbundle. We illustrate the general framework on symplectic manifolds by studying the universality of Hamiltonian dynamics on regular level sets via a class of embeddings.

We study several aspects of fillings for links of general isolated quotient singularities using Floer theory, including co-fillings, Weinstein fillings, strong fillings, exact fillings and exact orbifold fillings, focusing on the non-existence of exact fillings of contact links of isolated terminal quotient singularities. We provide an extensive list of isolated terminal quotient singularities whose contact links are not exactly fillable, including $��C^n�/��(�Z�/�2�)��$ for $��n�⩾�3�$, which settles a conjecture of Eliashberg, quotient singularities from general cyclic group actions and finite subgroups of $��S�U�\left(�2�\right)�$, and all terminal quotient singularities in complex dimension 3. We also obtain uniqueness of the orbifold diffeomorphism type of exact orbifold fillings of contact links of some isolated terminal quotient singularities.

For a compact subset $�K$ of a closed symplectic manifold $��(�M�,�\omega �)�$, we prove that $�K$ is heavy if and only if its relative symplectic cohomology over the Novikov field is nonzero. As an application, we show that if two compact sets are not heavy and Poisson commuting, then their union is also not heavy. A discussion on superheaviness together with some partial results is also included.

We develop and exposit some general algebra useful for working with certain algebraic structures that arise in stable homotopy theory, such as those encoding well-behaved theories of power operations for $�E_{\infty }$ ring spectra. In particular, we consider Quillen cohomology in the context of algebras over algebraic theories, plethories, and Koszul resolutions for algebras over additive theories. By combining this general algebra with obstruction-theoretic machinery, we obtain tools for computing with $�E_{\infty }$ algebras over $�F_p$ and over Lubin–Tate spectra. As an application, we demonstrate the existence of $�E_{\infty }$ periodic complex orientations at heights $��h�⩽�2�$.