Related papers: Real secondary index theory

In this paper, we give a geometric expression for the multiplicities of the equivariant index of a spin-c Dirac operator.

We define an equivariant index of Spin$^c$-Dirac operators on possibly noncompact manifolds, acted on by compact, connected Lie groups. The main result in this paper is that the index decomposes into irreducible representations according to…

For smooth projective curves the Clifford index is an important invariant which provides a bound for the dimension of the space of sections of a line bundle. This is the first step in distinguishing curves of the same genus. In this paper…

In the previous papers, Furuta, Yoshida and the author gave a definition of analytic index theory of Dirac-type operator on open manifolds by making use of some geometric structure on an open covering of the end of the open manifold and a…

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…

We study the clustering of the lowest non negative eigenvalue of the Dirac operator on a general Dirac bundle when the metric structure is varied. In the classical case we show that any closed spin manifold of dimension greater than or…

In gravitation theory, the realistic fermion matter is described by spinor bundles associated with the cotangent bundle of a world manifold $X$. In this case, the Dirac operator can be introduced. There is the 1:1 correspondence between…

Let $\pi\cln X\to \Delta^m$ be a proper smooth K\"ahler morphism from a complex manifold $X$ to the unit polydisc $\Delta^m$. Suppose the fibers over the complement of a proper analytic subset are biholomorphic to a fixed projective…

We introduce a simplified (coarse) version of pseudo-differential calculus for operators of order zero on complete Riemannian manifolds. This calculus works for the usual Hormander (1,0) class of operators, as well as for…

This paper presents algebraic methods for the study of polynomial relative invariants, when the group G formed by the symmetries and relative symmetries is a compact Lie group. We deal with the case when the subgroup H of symmetries is…

In this article, we prove that on any compact spin manifold of dimension m congruent 0,6,7 mod 8, there exists a metric, for which the associated Dirac operator has at least one eigenvalue of multiplicity at least two. We prove this by…

We define a Real version of smooth Deligne cohomology for manifolds with involution which interpolates between equivariant sheaf cohomology and smooth imaginary-valued forms. Our main result is a classification of Real line bundles with…

We consider a generalisation of the Seiberg-Witten invariant to the families Seiberg-Witten invariants of a smooth family of 4-manifolds with fibres diffeomorphic to a 4-manifold $X$. Of particular interest is the special case when the…

Any oriented 4-dimensional real vector bundle is naturally a line bundle over a bundle of quaternion algebras. In this paper we give an account of modules over bundles of quaternion algebras, discussing Morita equivalence, characteristic…

In a basic framework of a complex Hilbert space equipped with a complex conjugation and an involution, linear operators can be real, quaternionic, symmetric or anti-symmetric, and orthogonal projections can furthermore be symplectic. This…

The problem we are considering came up in connection with the classification of singularities in positive characteristic. Then it is important that certain invariants like the determinacy can be bounded simultaneously in families of formal…

We introduce a $\mathbb{C}/\mathbb{Z}$-valued invariant of a foliated manifold with a stable framing and with a partially flat vector bundle. This invariant can be expressed in terms of integration in differential $K$-theory, or…

In this paper, we use skein-theoretic techniques to classify all virtual knot polynomials and trivalent graph invariants with certain smallness conditions. The first half of the paper classifies all virtual knot polynomials giving…

We obtain the topological obstructions to existence of a bundle of irreducible real Clifford modules over a pseudo-Riemannian manifold $(M,g)$ of arbitrary dimension and signature and prove that bundles of Clifford modules are associated to…

Since their introduction in 1994, the Seiberg-Witten invariants have become one of the main tools used in 4-manifold theory. In this thesis, we will use these invariants to identify sufficient conditions for a 3-manifold to fibre over a…