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2 edition of Holomorphic families of immersions and higher analytic torsion forms found in the catalog.

Holomorphic families of immersions and higher analytic torsion forms

Jean-Michel Bismut

# Holomorphic families of immersions and higher analytic torsion forms

## by Jean-Michel Bismut

Written in English

Subjects:
• Structures kählériennes.,
• Immersions (mathématiques).,
• Fibrés vectoriels.,
• Kählerian structures.,
• Immersions (Mathematics),
• Vector bundles.

• Edition Notes

Includes bibliographical references (p. [273]-275).

The Physical Object ID Numbers Statement Jean-Michel Bismut. Series Astérisque -- 244. Pagination vii, 275 p. ; Number of Pages 275 Open Library OL17697159M

adshelp[at] The ADS is operated by the Smithsonian Astrophysical Observatory under NASA Cooperative Agreement NNX16AC86ACited by: 2. Chapter 3 Torsion Introduction Torsion: twisting of a structural member, when it is loaded by couples that produce rotation about its longitudinal axis T1 = P1 d1 T2 = P2 d2 the couples T1, T2 are called torques, twisting couples or twisting moments unit of T: File Size: 1MB.

giving rise to a holomorphic family of immersions and deformed a ne special K ahler man-ifolds, which combine into a complex manifold M^ = M C. By pulling back the standard Hermitian form of V, the space M^ becomes equipped with a K ahler metric gand a at torsion free connection rwhich we use to de ne special real coordinates. Taking the Leg-. $\begingroup$ Dear David: A hint of the interaction with rep'n theory is already seen in the fact that the classical upper half-plane is a coset space for the Lie group ${\rm{GL}}_2(\mathbf{R})$, and relation of C-R eqns with Casimir in Lie alg., but need a more adelic formulation to see how the Hecke theory comes out from the action of a group also.. (Toy version: adelic formulation of.

Immersions associated with holomorphic germs: In this paper we fix a sign of the Smale invariant and we show that for immersions induced by holomorphic gems the sign-refined Smale invariant is the negative of the number of cross caps appearing in a generic perturbation of \Phi. Using the algebraic method we calculate it for some families of. given assumptions on Y). Using the higher analytic torsion deﬁned in [12], one can deﬁne a push-forward map g ∗: Kb 0(Y) → Kb 0(B); its determinant is represented in Kb 0(B) by the determinant of the cohomology, endowed with the Quillen metric. The main result of the following paper is to give a File Size: KB.

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### Holomorphic families of immersions and higher analytic torsion forms by Jean-Michel Bismut Download PDF EPUB FB2

Get this from a library. Holomorphic families of immersions and higher analytic torsion forms. [Jean-Michel Bismut]. Holomorphic Families of Immersions and Higher Analytic Torsion Forms Séminaire Bourbaki, volume /97, exposés Exposé Bourbaki.

Familles d'immersions holomorphes et formes de torsion analytique équivariantes Families of equivariant immersions and analytic torsion forms. J.-M. BismutHolomorphic families of immersions and higher analytic torsion forms.

Astérisque, (), p. viii+ Google by: 3. These forms generalize in any degree the analytic torsion of Ray and Singer. In the case of acyclic complexes of holomorphic Hermitian vector bundles, such forms are calculated by means of Bott. We construct analytic torsion forms for line bundles on holomorphic fibrations by tori, which are not necessarily Kähler fibrations.

This is done by double transgressing the top Chern class. The forms are given in terms of Epstein zeta functions. Also, we establish a corresponding double transgression formula and an anomaly by: 1. Holomorphic and de Rham torsion.

Holomorphic families of immersions and higher analytic torsion forms. Article. Jan in the spirit of the book, of Bismut's Local Family Index Theorem.

Jean-Michel Bismut, Holomorphic families of immersions and higher analytic torsion forms, Astérisque (), viii+ MR [B04a] Jean-Michel Bismut, Holomorphic and de Rham torsion, Compos.

This holomorphic analytic torsion and its generalizations are the main object of study of the present paper. Since this is the only kind of analytic torsion that we will consider, throughout the paper, by analytic torsion we will mean holomorphic analytic torsion.

In the paper [40], Quillen, using the analytic torsion, associated to each. Holomorphic and de Rham torsion - Volume Issue 5 - Jean-Michel Bismut.

Close this message to accept Cited by: 5. Deﬁnition In the special case that T is the higher analytic torsion form associated to the closed odd-dimensional oriented manifold Mand the acyclic locally constant sheaf of Hilbert spaces F deﬁned in Section 1 we denote the class hT by T (M,F).

3 Lie algebra cohomology classes of X(M) Recall that X(M) is the Lie algebra of Diff(M)0. [9] (with J. Lott) Flat vector bundles, direct images and higher real analytic torsion.

J.A.M.S. 8, () [10] Holomorphic families of immersions and higher analytic torsion forms. pp Astérisque n° SMF Paris [11] Local index theory, eta invariants and holomorphic torsion. Proceedings of the International.

J.-M. Bismut, Holomorphic Families of Immersions and Higher Analytic Torsion Forms, AstérisqueSociété Mathématique de France, Paris, zbMATH Google Scholar [BM] J.-M.

Bismut and X. Ma, Holomorphic immersions and equivariant torsion forms, J. Reine by: 9. Jean-Michel Bismut, Equivariant immersions and Quillen metrics, J. Differential Geom. 41 (), no. 1, 53– MR ; 7. Jean-Michel Bismut, Holomorphic families of immersions and higher analytic torsion forms, Astérisque (), viii+ MR ; 8.

On Holomorphic Immersions into K˜ahler Manifolds of Constant Holomorphic Sectional Curvature Ngaiming Mok⁄ Abstract. We study holomorphic immersions f: X.

M from a complex mani- fold X into a K˜ahler manifold of constant holomorphic sectional curvature M, i.e., a complex hyperbolic space form, a complex Euclidean space form, or the complex.

Les formes de torsion holomorphes du complexe de de Rham The holomorphic torsion forms of the de Rham complex. we announce the vanishing of the holomorphic torsion forms of the relative de Rham complex of an equivariant fibration.

J.-M. BismutHolomorphic families of immersions and higher analytic torsion : Jean-Michel Bismut. ASYMPTOTIC TORSION AND TOEPLITZ OPERATORS - Volume 16 Issue 2 - Jean-Michel Bismut, Xiaonan Ma, Weiping Zhang Regularity of the analytic torsion form on families of normal coverings.

Pacific Journal of Mathematics, Vol.Issue. 1, p. Holomorphic families of immersions and higher analytic torsion forms, Astérisque ( Cited by: [5] Bismut, Jean-Michel Holomorphic families of immersions and higher analytic torsion forms, Astérisque () no. viii+ pages | MR | Zbl [6] Bismut, Jean-Michel; Gillet, Henri; Soulé, Christophe Analytic torsion and holomorphic determinant by:   Last, we obtain the gluing formula of analytic torsion forms through that of the combinatorial torsion form in certain sense.

In Sectionwe state a key result, Theoremwhich will be proved in the next subsections. Then we establish the gluing formula of analytic torsion forms.

The remaining sections are all devoted to prove Theorem Cited by: 2. Flat vector bundles, direct images and higher real analytic torsion: From probability to geometry: volume in honor of the 60th birthday of Jean-Michel Bismut: Groupoïdes de déformations et applications.

Holomorphic families of immersions and higher analytic torsion forms. Local Index Theory and Higher Analytic Torsion Dolbeault complex, a spectral invariant of the Hodge Laplacians along the ﬁbres. It was used by Quillen [49] to construct a metric on (det(Rπ∗E))−1, whose properties were studied by Quillen [49], and by Gillet, Soul´e and the author [17].

Immersions (Mathematics) 27 works Search for books with subject Immersions (Mathematics). Search. Holomorphic families of immersions and higher analytic torsion forms Jean-Michel Bismut Read.

Read. Read. Isometric immersions and embeddings of locally Euclidean metrics I. Kh Sabitov.1 Analytic torsion - from algebra to analysis - the nite-dimensional case Torsion of chain complexes Let kbe a eld. If Vis a nite-dimensional k-vector space and A: V!Van isomorphism, then we have the determinant detA2k.

The torsion of a chain complex is a generalization of the determinant as we will explain next.References top [AlGBMNV] ALVAREZ-GAUMÉ L., BOST J.

B., MOORE G., NELSON P., VAFA C., Bosonization on higher genus Riemann surfaces, Comm. Math. Phys., ( Cited by: