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We prove that a rational linear combination of Chern numbers is an oriented diffeomorphism invariant of smooth complex projective varieties if and only if it is a linear combination of the Euler and Pontryagin numbers. In dimension at least…

Geometric Topology · Mathematics 2011-11-24 D. Kotschick

Motivic integration and MacPherson's transformation are combined in this paper to construct a theory of "stringy" Chern classes for singular varieties. These classes enjoy strong birational invariance properties, and their definition…

Algebraic Geometry · Mathematics 2007-05-23 Tommaso de Fernex , Ernesto Lupercio , Thomas Nevins , Bernardo Uribe

In this paper, we construct for higher twists that arise from cohomotopy classes, the Chern character in higher twisted K-theory, that maps into higher twisted cohomology. We show that it gives rise to an isomorphism between higher twisted…

Differential Geometry · Mathematics 2021-06-23 Lachlan Macdonald , Varghese Mathai , Hemanth Saratchandran

We develop a theory of ``ad hoc'' Chern characters for twisted matrix factorizations associated to a scheme $X$, a line bundle ${\mathcal L}$, and a regular global section $W \in \Gamma(X, {\mathcal L})$. As an application, we establish the…

Algebraic Geometry · Mathematics 2014-04-02 Mark E. Walker

We discuss a class of 3-dimensional N=4 Chern-Simons (CS) quiver gauge models obtained from M-theory compactifications on singular complex 4-dimensional hyper-Kahler (HK) manifolds, which are realized explicitly as a cotangent bundle over…

High Energy Physics - Theory · Physics 2012-10-25 Adil Belhaj , Pablo Diaz , Maria Pilar Garcia del Moral , Antonio Segui

We study the homotopy aspects of the twisted Chern classes of torsion bundle gerbe modules. Using Sullivan's rational homotopy theory, we realize the twisted Chern classes at the level of classifying spaces. The construction suggests a…

Algebraic Topology · Mathematics 2022-03-29 Fei Han , Ruizhi Huang , Varghese Mathai

For a compact Lie group acting on a smooth manifold, we define the differential cohomology of a certain quotient stack involving principal bundles with connection. This produces differential equivariant cohomology groups that map to the…

Algebraic Topology · Mathematics 2016-08-04 Corbett Redden

We construct three simplicial presheaves on the site of ringed spaces, and in particular on that of complex manifolds. The descent objects for these simplicial presheaves yield Toledo--Tong's twisting cochains, simplicial twisting cochains,…

Algebraic Geometry · Mathematics 2025-12-16 Timothy Hosgood , Mahmoud Zeinalian

This article is concerned with Chern class and Chern number inequalities on polarized manifolds and nef vector bundles. For a polarized pair $(M,L)$ with $L$ very ample, our first main result is a family of sharp Chern class inequalities.…

Differential Geometry · Mathematics 2022-05-11 Ping Li , Fangyang Zheng

We begin by explaining how a physical problem of studying the quantum Hall effect on a closed surface $C$ leads, via Laughlin's approach, to a mathematical question of describing the rank and the first Chern class of a particular vector…

Algebraic Geometry · Mathematics 2025-06-30 Semyon Klevtsov , Dimitri Zvonkine

We describe the second integral cohomology group of a surface bundle as the group of Chern classes of fiberwise holomorphic complex line bundles and use this to obtain information on this group.

Geometric Topology · Mathematics 2020-08-31 Ursula Hamenstädt

Several authors have recently constructed characteristic classes for classes of infinite rank vector bundles appearing in topology and physics. These include the tangent bundle to the space of maps between closed manifolds, the infinite…

K-Theory and Homology · Mathematics 2011-07-26 Andres Larrain-Hubach

If I is a nilpotent ideal in a $\mathbb{Q}$-algebra $A$, Goodwillie defined two isomorphisms from $K_*(A,I)$ to negative cyclic homology, $HN_*(A,I)$. One is the relative version of the absolute Chern character, and the other is defined…

K-Theory and Homology · Mathematics 2011-08-03 Guillermo Cortiñas , Charles Weibel

Given a compact hyperkaehler manifold $M$ and a holomorphic bundle B over $M$, we consider a Hermitian connection $\nabla$ on B which is compatible with all complex structures on $M$ induced by the hyperkaehler structure. Such a connection…

alg-geom · Mathematics 2012-12-11 Misha Verbitsky

We exhaustively classify topological equivariant complex vector bundles over two-torus under a compact Lie group (not necessarily effective) action. It is shown that inequivariant Chern classes and isotropy representations at (at most) six…

Group Theory · Mathematics 2010-07-13 Min Kyu Kim

In previous work we generalised both the odd and even local index formula of Connes and Moscovici to the case of spectral triples for a *-subalgebra \A of a general semifinite von Neumann algebra. Our proofs are novel even in the setting of…

Operator Algebras · Mathematics 2007-05-23 Alan L. Carey , John Phillips , Adam Rennie , Fyodor A. Sukochev

In this note we define Chern-Simons classes of a superconnection $D+L$ on a complex supervector bundle $E$ such that $D$ is flat and preserves the grading, and $L$ is an odd endomorphism of $E$ on a supermanifold. As an application we…

Algebraic Geometry · Mathematics 2007-07-17 JN Iyer , Un Iyer

In this paper we define tensor modules(sheaves) of Schur type,or of generalized Schur type associated with the give module(sheaf), using the so-called Schur functors. Then using global method we construct canonical homomorphisms between…

Algebraic Geometry · Mathematics 2012-07-17 Jianke Chen

We present the construction of a Chern character in cyclic cohomology, involving an arbitrary number of associative algebras in contravariant or covariant position. This is a generalization of the bivariant Chern character for bornological…

Mathematical Physics · Physics 2007-05-23 Denis Perrot

We calculate the Chern classes and Chern numbers for the natural almost Hermitian structures of the partial flag manifolds F_n=SU(n+2)/S(U(n)\times U(1)\times U(1)). For all n>1 there are two invariant complex algebraic structures, which…

Differential Geometry · Mathematics 2013-01-29 D. Kotschick , S. Terzic