Extensions of Johnson's and Morita's homomorphisms that map to finitely generated abelian groups

We extend each higher Johnson homomorphism to a crossed homomorphism from the automorphism group of a finite-rank free group to a finite-rank abelian group. We also extend each Morita homomorphism to a crossed homomorphism from the mapping class group of once-bounded surface to a finite-rank abelian group. This improves on the author's previous results [Algebr. Geom. Topol. 7 (2007):1297-1326]. To prove the first result, we express the higher Johnson homomorphisms as coboundary maps in group cohomology. Our methods involve the topology of nilpotent homogeneous spaces and lattices in nilpotent Lie algebras. In particular, we develop a notion of the "polynomial straightening" of a singular homology chain in a nilpotent homogeneous space.Comment: 34 page

Trigonometric Sutherland systems and their Ruijsenaars duals from symplectic reduction

Besides its usual interpretation as a system of $n$ indistinguishable particles moving on the circle, the trigonometric Sutherland system can be viewed alternatively as a system of distinguishable particles on the circle or on the line, and these 3 physically distinct systems are in duality with corresponding variants of the rational Ruijsenaars-Schneider system. We explain that the 3 duality relations, first obtained by Ruijsenaars in 1995, arise naturally from the Kazhdan-Kostant-Sternberg symplectic reductions of the cotangent bundles of the group U(n) and its covering groups $U(1) \times SU(n)$ and ${\mathbb R}\times SU(n)$, respectively. This geometric interpretation enhances our understanding of the duality relations and simplifies Ruijsenaars' original direct arguments that led to their discovery.Comment: 34 pages, minor additions and corrections of typos in v

Classification and analysis of two dimensional abelian fractional topological insulators

We present a general framework for analyzing fractionalized, time reversal invariant electronic insulators in two dimensions. The framework applies to all insulators whose quasiparticles have abelian braiding statistics. First, we construct the most general Chern-Simons theories that can describe these states. We then derive a criterion for when these systems have protected gapless edge modes -- that is, edge modes that cannot be gapped out without breaking time reversal or charge conservation symmetry. The systems with protected edge modes can be regarded as fractionalized analogues of topological insulators. We show that previous examples of 2D fractional topological insulators are special cases of this general construction. As part of our derivation, we define the concept of "local Kramers degeneracy" and prove a local version of Kramers theorem.Comment: 19 pages, 2 figures, added reference, corrected typo

Particle Topology, Braids, and Braided Belts

Recent work suggests that topological features of certain quantum gravity theories can be interpreted as particles, matching the known fermions and bosons of the first generation in the Standard Model. This is achieved by identifying topological structures with elements of the framed Artin braid group on three strands, and demonstrating a correspondence between the invariants used to characterise these braids (a braid is a set of non-intersecting curves, that connect one set of $N$ points with another set of $N$ points), and quantities like electric charge, colour charge, and so on. In this paper we show how to manipulate a modified form of framed braids to yield an invariant standard form for sets of isomorphic braids, characterised by a vector of real numbers. This will serve as a basis for more complete discussions of quantum numbers in future work.Comment: 21 pages, 16 figure

Проблемы финансовых расследований и возврата похищенных активов

In the context of the globalization of national economies, the processes of recovering stolen assets are becoming a difficult task, requiring their tracing and detection not only in our country but also in foreign jurisdictions. Not only country’s law enforcement agencies but also corporate governance bodies should play an active role in the process of detecting and recovering stolen assets. In this regard, the improvement of methodological tools that facilitate the tracking, detection and recovery of stolen assets is of scientific and practical interest and ensures the relevance of the study. The purpose of the study is to improve the mechanisms for countering the withdrawal of assets by unscrupulous owners, interest groups. The authors apply methods of dialectical scientific cognition based on a set of recognized private scientific and general scientific methods: formal-logical, comparative-legal, statistical, intersectoral legal analysis. The scientific novelty of the research is the identification of negative factors affecting the volume of stolen assets, their impact on the economic health of the state, private sector, and the improvement of methods for detecting and recovering assets. The results of the study help the authors to identify the main problems of detection and recovery of stolen assets, formulated the directions of the strategy for the return of stolen assets, formalized the processes of tax administration in countering the legalization of illegally obtained property. The recovery of stolen assets is an extremely time-consuming process which requires not only collective action of government agencies but also effective interstate cooperation within the legal framework. The paper presents a comparative analysis of the legislation of a number of countries. The authors identify deficiencies in the Russian law, which does not fully prescribe the procedure for detecting and returning stolen assets to the territory of the country. The authors conclude that in order to improve the mechanisms for countering the withdrawal of assets, it is necessary to apply an integrated approach, improving the legislation of the Russian Federation and fostering collective action of the country’s law enforcement agencies, private sector, and society to successfully confront new challenges and threats. The results of the study may be used to improve the competence of law enforcement officers involved in detecting and returning stolen assets, as well as to develop a more successful methodological and evidence base approach in countering the legalization of illegally obtained property.В условиях глобализации национальных экономик процессы возврата похищенных активов становятся труднорешаемой задачей, требующей достоверной идентификации их места нахождения не только на территории нашей страны, но и за рубежом. Активную роль в процессе розыска и возврата похищенных активов должны играть не только правоохранительные органы страны, но и органы корпоративного управления. В связи с этим совершенствование методических инструментов по розыску, идентификации и возврату похищенных активов представляет научный и практический интерес, что подтверждает актуальность темы исследования. Цель исследования — совершенствование механизмов противодействия выводу активов недобросовестными собственниками, заинтересованной группой лиц. Авторы использовали методы диалектического научного познания, базирующиеся на совокупности признанных частно-научных и общенаучных методов: формально-логическом, сравнительно-правовом, статистическом, межотраслевого правового анализа. Научной новизной исследования является выделение негативных факторов, влияющих на объем похищаемых активов, их влияние на экономическое состояние государства, частного бизнеса, совершенствование методов поиска и возврата активов. В результате исследования выявлены основные проблемы идентификации и возврата похищенных активов, сформулированы направления стратегии возврата похищенных активов, формализованы процессы налогового администрирования в борьбе с легализацией незаконно приобретенного имущества. Показан процесс возврата похищенных активов как чрезвычайно трудоемкая работа, требующая слаженных действий не только государственных структур, но и эффективного межгосударственного сотрудничества на правовой основе. Сделан сравнительный анализ законодательства ряда стран. Выявлены недостатки в российском законодательстве, которые не в полной мере обеспечивают процедуру идентификации и возврата похищенных активов на территорию страны. Сделан вывод, что в целях совершенствования механизмов противодействия выводу активов необходимо использовать комплексный подход, основой которого является гармонизация законодательства Российской Федерации, объединения усилий правоохранительных органов страны, частного бизнеса и общества для успешного противостояния новым вызовам и угрозам. Результаты данного исследования можно использовать для повышения компетенций сотрудников правоохранительных органов, занимающихся идентификацией и возвратом похищенных активов, а также для более успешного формирования методической и доказательной базы в противодействии легализации незаконно приобретенного имущества