Let X be a compact real analytic manifold, and let T X be its cotangent bundle. In a recent paper with E. Zaslow [28], we showed that the dg category Shc(X) of constructible sheaves on X quasi-embeds into the triangulated envelope F (T X) of the Fukaya category of T X. We prove here that the quasi-embedding is in fact a quasi-equivalence. When X is a complex manifold, one may interpret this as ...

0. Introduction. This paper continues the study of the noncommutative innn-itesimal cohomology we introduced in 3]. This is the cohomology of sheaves on a noncommutative version of the commutative innnitesimal site of Grothendieck ((8]). Grothendieck showed that, for a smooth scheme X of characteristic zero, the cohomology of the structure sheaf on the innnitesimal site gives de Rham cohomol-og...

The purpose of this article is to show that the bivariant algebraic A-cobordism groups considered previously by author are independent chosen base ring A. This result proven analyzing ideal generated so called snc relations, and, while alternative characterization we obtain for interesting itself because its simplicity, perhaps more importantly it allows us easily extend definition cobordism di...

We use persistence modules and their corresponding barcodes to quantitatively distinguish between different fiberwise star-shaped domains in the cotangent bundle of a fixed manifold. The distance two is measured by nonlinear version classical Banach–Mazur distance, called symplectic denoted [Formula: see text]. relevant come from filtered homology are stable with respect Our main focus on space...

in this paper we investigate decompositions of submodules in modules over a proufer domain into intersections of quasi-primary and classical quasi-primary submodules. in particular, existence and uniqueness of quasi-primary decompositions in modules over a proufer domain of finite character are proved. proufer domain; primary submodule; quasi-primary submodule; classical quasi-primary; decomposi...

Hess and Shipley defined an invariant of coalgebra spectra called topological coHochschild homology, Bohmann–Gerhardt–Høgenhaven–Shipley–Ziegenhagen developed a coBökstedt spectral sequence to compute the homology $$\mathrm {coTHH}$$ for coalgebras over sphere spectrum. We construct relative study any commutative ring spectrum R. Further, we use algebraic structures in this complete some calcul...

We prove that Khovanov homology detects the trefoils. Our proof incorporates an array of ideas in Floer and contact geometry. It uses open books; invariants we defined instanton setting; a bypass exact triangle sutured homology, proven here; Kronheimer Mrowka's spectral sequence relating with singular knot homology. As byproduct, also strengthen result Mrowka on $SU(2)$ representations group.