ترغب بنشر مسار تعليمي؟ اضغط هنا

Equivariant relative Thom forms and Chern characters

96   0   0.0 ( 0 )
 نشر من قبل Paul-Emile Paradan
 تاريخ النشر 2007
  مجال البحث
والبحث باللغة English




اسأل ChatGPT حول البحث

These notes are the first chapter of a monograph, dedicated to a detailed proof of the equivariant index theorem for transversally elliptic operators. In this preliminary chapter, we prove a certain number of natural relations in equivariant cohomology. These relations include the Thom isomorphism in equivariant cohomology, the multiplicativity of the relative Chern characters, and the Riemann-Roch relation between the relative Chern character of the Bott symbol and of the relative Thom class.



قيم البحث

اقرأ أيضاً

We construct a map from $d|1$-dimensional Euclidean field theories to complexified K-theory when $d=1$ and complex analytic elliptic cohomology when $d=2$. This provides further evidence for the Stolz--Teichner program, while also identifying candida te geometric models for Chern characters within their framework. The construction arises as a higher-dimensional and parameterized generalization of Fei Hans realization of the Chern character in K-theory as dimensional reduction for $1|1$-dimensional Euclidean field theories. In the elliptic case, the main new feature is a subtle interplay between the geometry of the super moduli space of $2|1$-dimensional tori and the derived geometry of complex analytic elliptic cohomology. As a corollary, we obtain an entirely geometric proof that partition functions of $mathcal{N}=(0,1)$ supersymmetric quantum field theories are weak modular forms, following a suggestion of Stolz and Teichner.
A differential 1-form $alpha$ on a manifold of odd dimension $2n+1$, which satisfies the contact condition $alpha wedge (dalpha)^n eq 0$ almost everywhere, but which vanishes at a point $O$, i.e. $alpha (O) = 0$, is called a textit{singular contact form} at $O$. The aim of this paper is to study local normal forms (formal, analytic and smooth) of such singular contact forms. Our study leads naturally to the study of normal forms of singular primitive 1-forms of a symplectic form $omega$ in dimension $2n$, i.e. differential 1-forms $gamma$ which vanish at a point and such that $dgamma = omega$, and their corresponding conformal vector fields. Our results are an extension and improvement of previous results obtained by other authors, in particular Lychagin cite{Lychagin-1stOrder1975}, Webster cite{Webster-1stOrder1987} and Zhitomirskii cite{Zhito-1Form1986,Zhito-1Form1992}. We make use of both the classical normalization techniques and the toric approach to the normalization problem for dynamical systems cite{Zung_Birkhoff2005, Zung_Integrable2016, Zung_AA2018}.
129 - John Harvey 2014
Let a compact Lie group act isometrically on a non-collapsing sequence of compact Alexandrov spaces with fixed dimension and uniform lower curvature and upper diameter bounds. If the sequence of actions is equicontinuous and converges in the equivari ant Gromov--Hausdorff topology, then the limit space is equivariantly homeomorphic to spaces in the tail of the sequence. As a consequence, the class of Riemannian orbifolds of dimension $n$ defined by a lower bound on the sectional curvature and the volume and an upper bound on the diameter has only finitely many members up to orbifold homeomorphism. Furthermore, any class of isospectral Riemannian orbifolds with a lower bound on the sectional curvature is finite up to orbifold homeomorphism.
Motivated by our attempt to recast Cartans work on Lie pseudogroups in a more global and modern language, we are brought back to the question of understanding the linearization of multiplicative forms on groupoids and the corresponding integrability problem. From this point of view, the novelty of this paper is that we study forms with coefficients. However, the main contribution of this paper is conceptual: the finding of the relationship between multiplicative forms and Cartans work, which provides a completely new approach to integrability theorems for multiplicative forms. Back to Cartan, the multiplicative point of view shows that, modulo Lies functor, the Cartan Pfaffian system (itself a multiplicative form with coefficients!) is the same thing as the classical Spencer operator.
This paper generalizes Bismuts equivariant Chern character to the setting of abelian gerbes. In particular, associated to an abelian gerbe with connection, an equivariantly closed differential form is constructed on the space of maps of a torus into the manifold. These constructions are made explicit using a new local version of the higher Hochschild complex, resulting in differential forms given by iterated integrals. Connections to two dimensional topological field theories are indicated. Similarly, this local higher Hochschild complex is used to calculate the 2-holonomy of an abelian gerbe along any closed oriented surface, as well as the derivative of 2-holonomy, which in the case of a torus fits into a sequence of higher holonomies and their differentials.
التعليقات
جاري جلب التعليقات جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
mircosoft-partner

هل ترغب بارسال اشعارات عن اخر التحديثات في شمرا-اكاديميا