The Stasheff Model of a Simply-connected Manifold and the String Bracket
نویسنده
چکیده
We revisit Stasheff’s construction of a minimal Lie-Quillen model of a simplyconnected closed manifold M using the language of infinity-algebras. This model is then used to construct a graded Lie bracket on the equivariant homology of the free loop space of M minus a point similar to the Chas-Sullivan string bracket.
منابع مشابه
An Algebraic Chain Model of String Topology
A chain complex model for the free loop space of a connected, closed and oriented manifold is presented, and on its homology, the Gerstenhaber and Batalin-Vilkovisky algebra structures are defined and identified with the string topology structures. The gravity algebra on the equivariant homology of the free loop space is also modeled. The construction includes the non-simply connected case, and...
متن کاملNonlinear Dynamics of the Rotational Slender Axially Moving String with Simply Supported Conditions
In this research, dynamic analysis of the rotational slender axially moving string is investigated. String assumed as Euler Bernoulli beam. The axial motion of the string, gyroscopic force and mass eccentricity were considered in the study. Equations of motion are derived using Hamilton’s principle, resulting in two partial differential equations for the transverse motions. The equations are ch...
متن کاملForm field theory on Calabi-Yau threefold
We show how the natural Abelian duality of 2 and 3-form gravity theories in 7-dimensional manifold CY3 × S leads to an S-duality between 2 and 3-form theories on simply connected CY3. The massless sector of the 2-form field theory on CY3 corresponds to the A model string field theory. We discuss the complex structure independence of the 2 form theory for a general Kähler manifold and derive the...
متن کاملDe Rham model for string topology
0. Introduction. Let M be a simply connected closed oriented n-dimensional manifold, and LM := Map C ∞ (S 1 , M) the associated free loop space. String topology of Chas and Sul-livan [CS] deals with an ample family of algebraic operations on the ordinary and equivariant homologies of LM , the most important being a graded commutative associative product,
متن کاملThe Vanishing Problem of the String Class with Degree 3
Let 3⁄4 be an SO.n/-bundle over a simply connected manifold M with a spin structure Q ! M . The string class is an obstruction to lift the structure group LSpin.n/ of the loop group bundle L Q ! L M to the universal central extension of LSpin.n/ by the circle. We prove that the string class vanishes if and only if 1=2 the first Pontrjagin class of 3⁄4 vanishes when M is a compact simply connect...
متن کامل