Operadic twisting - With an application to Deligne's conjecture

被引：36

作者：

Dolgushev, Vasily ^{[1
]}

Willwacher, Thomas ^{[2
]}

机构：

[1] Temple Univ, Dept Math, Philadelphia, PA 19122 USA

[2] Univ Zurich, Inst Math, CH-8057 Zurich, Switzerland

来源：

JOURNAL OF PURE AND APPLIED ALGEBRA | 2015年 / 219卷 / 05期

基金：

美国国家科学基金会; 瑞士国家科学基金会;

关键词：

FORMALITY;

D O I：

10.1016/j.jpaa.2014.06.010

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We study categorial properties of the operadic twisting functor Tw. In particular, we show that Tw is a comonad. Coalgebras of this comonad are operads for which a natural notion of twisting by Maurer-Cartan elements exists. We give a large class of examples, including the classical cases of the Lie, associative and Gerstenhaber operads, and their infinity-counterparts Lie(infinity), As-infinity, Ger(infinity). We also show that Tw is well behaved with respect to the homotopy theory of operads. As an application we show that every solution of Deligne's conjecture is homotopic to a solution that is compatible with twisting. (C) 2014 Elsevier B.V. All rights reserved.

引用

页码：1349 / 1428

页数：80

共 33 条

[1]

[Anonymous], 2004, Contemp. Math.

[2]

BATANIN MA, ARXIV08032249

[3] Combinatorial operad actions on cochains [J].

Berger, C ;

Fresse, B .

MATHEMATICAL PROCEEDINGS OF THE CAMBRIDGE PHILOSOPHICAL SOCIETY, 2004, 137 :135-174

[4] Combinatorics and Formal Geometry of the Maurer-Cartan Equation [J].

Chuang, Joseph ;

Lazarev, Andrey .

LETTERS IN MATHEMATICAL PHYSICS, 2013, 103 (01) :79-112

[5] L-INFINITY MAPS AND TWISTINGS [J].

Chuang, Joseph ;

Lazarev, Andrey .

HOMOLOGY HOMOTOPY AND APPLICATIONS, 2011, 13 (02) :175-195

[6] Covariant and equivariant formality theorems [J].

Dolgushev, V .

ADVANCES IN MATHEMATICS, 2005, 191 (01) :147-177

[7] Proof of Swiss Cheese Version of Deligne's Conjecture [J].

Dolgushev, V. A. ;

Tamarkin, D. E. ;

Tsygan, B. L. .

INTERNATIONAL MATHEMATICS RESEARCH NOTICES, 2011, 2011 (20) :4666-4746

[8]

Dolgushev V.A., 2005, ARXIVMATH0504420 MIT

[9] Notes on algebraic operads, graph complexes, and Willwacher's construction [J].

Dolgushev, Vasily A. ;

Rogers, Christopher L. .

MATHEMATICAL ASPECTS OF QUANTIZATION, 2012, 583 :25-+

[10] Lie theory of formal groups over an operad [J].

Fresse, B .

JOURNAL OF ALGEBRA, 1998, 202 (02) :455-511

← 1 2 3 4 →