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We prove nilpotence theorems in tensor-triangulated categories using suitable Gabriel quotients of the module category, and discuss examples.

Category Theory · Mathematics 2019-08-14 Paul Balmer

We prove that the homotopy theory of Picard 2-categories is equivalent to that of stable 2-types.

Algebraic Topology · Mathematics 2019-05-01 Nick Gurski , Niles Johnson , Angélica M. Osorno

A theorem is proved to verify incremental stability of a feedback system via a homotopy from a known incrementally stable system. A first corollary of that result is that incremental stability may be verified by separation of Scaled…

Optimization and Control · Mathematics 2024-12-03 Thomas Chaffey , Andrey Kharitenko , Fulvio Forni , Rodolphe Sepulchre

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.

Differential Geometry · Mathematics 2015-07-17 Man-Ho Ho

The semigroup of the homotopy classes of the self-homotopy maps of a finite complex which induce the trivial homomorphism on homotopy groups is nilpotent. We determine the nilpotency of these semigroups of compact Lie groups and finite Hopf…

Algebraic Topology · Mathematics 2009-03-27 Ken-ichi Maruyama

In this short note, we prove a general nilpotence theorem for a rational rigid 2-ring all of whose objects satisfy a certain ``moderate growth condition'' inspired from the theory of tensor categories. This applies in particular to the…

Algebraic Geometry · Mathematics 2026-05-26 Logan Hyslop

We prove exponential stability theorems of Nekhoroshev type for motion in the neighbourhood of an elliptic fixed point in Hamiltonian systems having an additional transverse component of arbitrary dimension.

Dynamical Systems · Mathematics 2012-01-19 Markus Kunze , David Stuart

In this short note we prove that a saturated fusion system admitting some special type of automorphism is nilpotent. This generalizes classical results by J.G. Thompson.

Group Theory · Mathematics 2018-04-16 Jon González-Sánchez , Albert Ruiz , Antonio Viruel

This paper starts by showing that for algebras in a certain class the concepts of weak nilpotency and nilpotency coincide. It goes on to describe some solvability and nilpotency properties of bicommutative algebras, of assosymmetric and of…

Rings and Algebras · Mathematics 2024-08-21 David A. Towers

Supernilpotence is a generalization of nilpotence using a recently developed theory of higher-arity commutators for universal algebras. Many important structural properties have been shown to be associated with supernilpotence, and the…

Rings and Algebras · Mathematics 2018-08-17 Matthew Moore , Andrew Moorhead

We study the homotopy groups of open books in terms of those of their pages and bindings. Under homotopy theoretic conditions on the monodromy we prove an integral decomposition result for the based loop space on an open book, and under…

Algebraic Topology · Mathematics 2024-09-17 Ruizhi Huang , Stephen Theriault

In this note, we give a new proof by module-theoretic methods for a result of Puig asserting that blocks which are stable equivalent of Morita type to nilpotent blocks are also nilpotent.

Representation Theory · Mathematics 2024-05-29 Conghui Li

We prove a stability theorem for families of holomorphically-parallelizable manifolds in the category of Hermitian manifolds.

Complex Variables · Mathematics 2015-07-13 Daniele Angella , Adriano Tomassini

An introduction and survey of homotopy type theory in honor of W.W. Tait.

Logic · Mathematics 2023-03-31 Steve Awodey

We introduce coherent cohomology theories h_* and prove that if such a theory is moreover generically constant then the Rost nilpotence principle holds for projective homogeneous varieties in the category of h_*-motives. Examples of such…

Algebraic Geometry · Mathematics 2018-11-28 Stefan Gille , Alexander Vishik

Answering a question posed by Bergelson and Leibman in [6], we establish a nilpotent version of the polynomial Hales-Jewett theorem that contains the main theorem in [6] as a special case. Important to the formulation and the proof of our…

Combinatorics · Mathematics 2018-11-26 John H. Johnson , Florian Karl Richter

We note a parallel between some ideas of stable model theory and certain topics in finite combinatorics related to the sum-product phenomenon. For a simple linear group G, we show that a finite subset X with |X X \^{-1} X |/ |X| bounded is…

Logic · Mathematics 2011-05-17 Ehud Hrushovski

In recent work a multimonopole solution of heterotic string theory was obtained. The monopoles are noted to be stable, in contrast with analogous solutions of Einstein-Maxwell or Yang-Mills-dilaton theory. The existence of this and other…

High Energy Physics - Theory · Physics 2009-10-22 Ramzi R. Khuri

This paper contains an overview of background from stable homotopy theory used by Freed--Hopkins in their work on invertible extended topological field theories. We provide a working guide to the stable homotopy category, to the Steenrod…

Algebraic Topology · Mathematics 2018-05-10 Agnes Beaudry , Jonathan A. Campbell

To every homotopy n-nilpotent group, defined in earlier work by Dwyer and the author, we associate an endofunctor of pointed spaces and prove that it is looped and n-excisive. As a tool we prove that $\Omega P_n({\rm id})$ commutes with…

Algebraic Topology · Mathematics 2017-05-16 Georg Biedermann