Related papers: An index theorem for gerbes
We give a proof for the fundamental theorem of algebra,using the Fredholm index phenomena
In this paper we prove several theorems about the behavior of index of Lie algebras derived from associative algebras under tensor products of underlying associative algebras.
In this paper we give a proof of an index theorem by Bismut. As a consequence we obtain another proof of the Grothendieck-Riemann-Roch theorem in differential cohomology.
We offer streamlined proofs of fundamental theorems regarding the index theory for partial self-maps of an infinite set that are bijective between cofinite subsets.
We prove a Morse index theorem for action functionals on paths that are allowed to reflect at a hypersurface (either in the interior or at the boundary of a manifold). Both fixed and periodic boundary conditions are treated.
In this paper we prove a relative index theorem for pairs of generalized Dirac operators on orbifolds which are the same at infinity. This generalizes to orbifolds a celebrated theorem of Gromov and Lawson.
In this paper, we prove a Morse index theorem for the index form of regular Lagrangian system with selfadjoint boundary condition.
It seems that the index theory for non-compact spaces has found its ultimate formulation in realm of coarse spaces and $K$-theory of related operator algebras. Relative and partitioned index theorems may be mentioned as two important and…
In this paper, we prove a Morse index theorem for the index form of even order linear Hamiltonian systems on the closed interval with reasonable self-adjoint boundary conditions. The highest order term is assumed to be nondegenerate.
In this note we give a detailed proof of a theorem of Aubin.
We show how tools from computational group theory can be used to prove that a subgroup of matrices has infinite index.
We prove an analog of Gromov--Lawson type relative index theorems for K-homology classes.
We prove Shokurov's index conjecture for quotient singularities.
We present a relative form of the Toponogov comparison theorem.
The use of bundle gerbes and bundle gerbe modules is considered as a replacement for the usual theory of Clifford modules on manifolds that fail to be spin. It is shown that both sides of the Atiyah-Singer index formula for coupled Dirac…
This thesis develops the theory of bundle gerbes and examines a number of useful constructions in this theory. These allow us to gain a greater insight into the structure of bundle gerbes and related objects. Furthermore they naturally lead…
Index theorem is formulated in noncommutative geometry with finite degrees of freedom by using Ginsparg-Wilson relation. It is extended to the case where the gauge symmetry is spontaneously broken. Dynamical analysis about topological…
This paper introduces a notion of fundamental group appropriate for laminations.
We compute the index of a Lie Borel Lie Algbra of a simple Lie algebra.
We prove the Jones Index Theorem using the K-theory of a cluster $C^*$-algebra of the Riemann sphere with two boundary components.