Massey Products for Graph Homology
نویسندگان
چکیده
Abstract This paper shows that the operad encoding modular operads is Koszul. Using this result, we construct higher composition operations on (hairy) graph homology, which characterize its rational homotopy type.
منابع مشابه
Massey Products and Deformations
It is common knowledge that the construction of one-parameter deformations of various algebraic structures, like associative algebras or Lie algebras, involves certain conditions on cohomology classes, and that these conditions are usually expressed in terms of Massey products, or rather Massey powers. The cohomology classes considered are those of certain differential graded Lie algebras (DGLA...
متن کاملSplitting Varieties for Triple Massey Products
We construct splitting varieties for triple Massey products. For a, b, c ∈ F∗ the triple Massey product 〈a, b, c〉 of the corresponding elements of H(F, μ2) contains 0 if and only if there is x ∈ F∗ and y ∈ F[ √ a, √ c]∗ such that bx = NF[a,c]/F(y), where NF[ √ a, √ c]/F denotes the norm, and F is a field of characteristic different from 2. These varieties satisfy the Hasse principle by a result...
متن کاملMassey Products and Critical Points
In this paper we use cup-products and higher Massey products to find topological lower bounds on the minimal number of geometrically distinct critical points of any closed 1-form in a given cohomology class.
متن کاملMassey and Fukaya Products on Elliptic Curves
This note is a continuation of [6]. Its goal is to show that some higher Massey products on elliptic curve can be computed as higher compositions in Fukaya category of the dual symplectic torus in accordance with the homological mirror conjecture of M. Kontsevich [4]. Namely, we consider triple Massey products of very simple type which are uniquely defined, compute them in terms of theta-functi...
متن کاملMassey Products of Complex Hypersurface Complements
The study of the topology of hypersurface complements is a classical subject in algebraic geometry. Most of what is known about these spaces is related to invariants of their rational homotopy type. In this paper, we attempt to show that their Fp-homotopy type captures in general more information than the Q-homotopy type, where Fp is the prime field of p elements. Let X be the complement to a h...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: International Mathematics Research Notices
سال: 2021
ISSN: ['1687-0247', '1073-7928']
DOI: https://doi.org/10.1093/imrn/rnaa346