Related papers: Relative-partitioned index theorem

We identify computability-theoretic properties enabling us to separate various statements about partial orders in reverse mathematics. We obtain simpler proofs of existing separations, and deduce new compound ones. This work is part of a…

In this sequence, we first prove an abstract Morse index theorem in a Hilbert space modeling a variational problem with constraints. Then, our abstract formulation is applied to study several optimization setups including closed CMC…

We show that every quasi-compact and quasi-separated algebraic stack can be approximated by a noetherian algebraic stack. We give several applications such as eliminating noetherian hypotheses in the theory of good moduli spaces.

This book is mainly an exposition of the author's works and his joint works with his former students on explicit representations of finite-dimensional simple Lie algebras, related partial differential equations, linear orthogonal algebraic…

The central purpose of this article is to establish new inverse and implicit function theorems for differentiable maps with isolated critical points. One of the key ingredients is a discovery of the fact that differentiable maps with…

In this short note we present several infinite dimensional theorems which generalize corresponding facts from the finite dimensional differential inclusions theory.

We present assembly-theory, a Rust package for computing assembly indices of covalently bonded molecular structures. This is a key complexity measure of assembly theory, a recent theoretical framework quantifying selection across diverse…

By a [$K$-]approximate subring of a ring we mean an additively symmetric subset $X$ such that $X \cdot X \cup (X + X)$ is covered by finitely many [resp.\ $K$] additive translates of $X$. We prove a structure theorem for finite approximate…

We study the K-theory of ring C*-algebras associated to rings of integers in global function fields with only one single infinite place. First, we compute the torsion-free part of the K-groups of these ring C*-algebras. Secondly, we show…

We develop a new framework of relative algebroids to address existence and classification problems of geometric structures subject to partial differential equations.

We prove a super-version of Nest-Tsygan's algebraic index theorem. This work is inspired by the appearance of the same cobordism invariants in three related stories: index theory, trace methods in the deformation theory of algebras, and…

We prove an analytic KAM-Theorem, which is used in [1], where the differential part of KAM-theory is discussed. Related theorems on analytic KAM-theory exist in the literature (e. g., among many others, [7], [8], [13]). The aim of the…

The investigation of partitions of integers plays an important role in combinatorics and number theory. Among the many variations, partitions into powers $0<\alpha<1$ were of recent interest. In the present paper we want to extend our…

We develop a theory of ordered *-vector spaces with an order unit. We prove fundamental results concerning positive linear functionals and states, and we show that the order (semi)norm on the space of self-adjoint elements admits multiple…

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…

We define an analytic index and prove a topological index theorem for a non-compact manifold $M\_0$ with poly-cylindrical ends. We prove that an elliptic operator $P$ on $M\_0$ has an invertible perturbation $P+R$ by a lower order operator…

We define an index of compatibility for a probabilistic theory (PT). Quantum mechanics with index 0 and classical probability theory with index 1 are at the two extremes. In this way, quantum mechanics is at least as incompatible as any PT.…

In this paper we address the decision problem for a fragment of set theory with restricted quantification which extends the language studied in [4] with pair related quantifiers and constructs, in view of possible applications in the field…

We define the filtrated K-theory of a C*-algebra over a finite topological space X and explain how to construct a spectral sequence that computes the bivariant Kasparov theory over X in terms of filtrated K-theory. For finite spaces with…

In the paper, notions of relative separability for hypergraphs of models of a theory are defined. Properties of these notions and applications to ordered theories are studied: characterizations of relative separability both in a general…