Wheel graph homology classes via Lie graph homology

نویسندگان

چکیده

We give a new proof of the non-triviality wheel graph homology classes using higher operations on Lie and derived version Koszul duality for modular operads.

برای دانلود باید عضویت طلایی داشته باشید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Graph homology and graph configuration spaces

If R is a commutative ring, M a compact R-oriented manifold and G a finite graph without loops or multiple edges, we consider the graph configuration space MG and a Bendersky–Gitler type spectral sequence converging to the homology H∗(M, R). We show that its E1 term is given by the graph cohomology complex CA(G) of the graded commutative algebra A = H∗(M, R) and its higher differentials are obt...

متن کامل

Homology and modular classes of Lie algebroids

For a Lie algebroid, divergences chosen in a classical way lead to a uniquely defined homology theory. They define also, in a natural way, modular classes of certain Lie algebroid morphisms. This approach, applied for the anchor map, recovers the concept of modular class due to S. Evens, J.-H. Lu, and A. Weinstein.

متن کامل

Delineating Homology Generators in Graph Pyramids

Computation of homology generators using a graph pyramid can significantly increase performance, compared to the classical methods. First results in 2D exist and show the advantages of the method. Generators are computed on the upper level of a graph pyramid. Toplevel graphs may contain self loops and multiple edges, as a side product of the contraction process. Using straight lines to draw the...

متن کامل

Graph Homology: Koszul and Verdier Duality

We show that Verdier duality for certain sheaves on the moduli spaces of graphs associated to Koszul operads corresponds to Koszul duality of operads. This in particular gives a conceptual explanation of the appearance of graph cohomology of both the commutative and Lie types in computations of the cohomology of the outer automorphism group of a free group. Another consequence is an explicit co...

متن کامل

Persistent homology in graph power filtrations

The persistence of homological features in simplicial complex representations of big datasets in R n resulting from Vietoris-Rips or Čech filtrations is commonly used to probe the topological structure of such datasets. In this paper, the notion of homological persistence in simplicial complexes obtained from power filtrations of graphs is introduced. Specifically, the rth complex, r ≥ 1, in su...

متن کامل

ذخیره 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: Journal of Noncommutative Geometry

سال: 2023

ISSN: ['1661-6960', '1661-6952']

DOI: https://doi.org/10.4171/jncg/508