Intersection Numbers and the Statement of the Disc Embedding Theorem

2021 ◽  
pp. 155-170
Author(s):  
Mark Powell ◽  
Arunima Ray
Keyword(s):  
Fundamental Group ◽  
Detailed Analysis ◽  
Group Ring ◽  
Embedding Theorem ◽  
Ambient Space ◽  
Intersection Numbers

‘Intersection Numbers and the Statement of the Disc Embedding Theorem’ provides detailed definitions of some of the notions involved in the statement of the disc embedding theorem, focusing specifically on intersection numbers. The chapter begins with a detailed analysis of immersions, regular homotopies, finger moves, and Whitney moves. Then it defines intersection and self-intersection numbers for families of discs and spheres, taking values in the group ring of the fundamental group of the ambient space, with the correct relations. Then it enumerates certain properties of intersection numbers, in particular relating them to the existence of Whitney discs. This work enables the disc embedding theorem to be stated carefully.

scholarly journals Surgery on closed 4-manifolds with free fundamental group

2002 ◽  
Vol 133 (2) ◽  
pp. 305-310 ◽  
Author(s):  
VYACHESLAV S. KRUSHKAL ◽  
RONNIE LEE
Keyword(s):  
Fundamental Group ◽  
Free Groups ◽  
Embedding Theorem ◽  
Topological Category ◽  
Subexponential Growth ◽  
Recent Developments ◽  
Simply Connected

The 4-dimensional topological surgery conjecture has been established for a class of groups, including the groups of subexponential growth (see [6], [13] for recent developments), however the general case remains open. The full surgery conjecture is known to be equivalent to the question for a class of canonical problems with free fundamental group [5, chapter 12]. The proof of the conjecture for ‘good’ groups relies on the disk embedding theorem (see [5]), which is not presently known to hold for arbitrary groups. However, in certain cases it may be shown that surgery works even when the disk embedding theorem is not available for a given fundamental group (such results still use the disk-embedding theorem in the simply-connected setting, proved in [3]). For example, this is possible when the surgery kernel is represented by π1-null spheres [4], or more generally by a π1-null submanifold satisfying a certain condition on Dwyer's filtration on second homology [7]. Here we state another instance when the surgery conjecture holds for free groups. The following results are stated in the topological category.

scholarly journals THE GENERALIZED DEHN TWIST ALONG A FIGURE EIGHT

2013 ◽  
Vol 05 (03) ◽  
pp. 271-295
Author(s):  
YUSUKE KUNO
Keyword(s):  
Fundamental Group ◽  
Group Ring ◽  
Boundary Component ◽  
Double Point ◽  
Dehn Twist ◽  
Oriented Surface ◽  
The Right

For any unoriented loop on a compact connected oriented surface with one boundary component, we introduce a generalized Dehn twist along the loop as a certain automorphism of the completed group ring of the fundamental group of the surface. If the loop is simple, this corresponds to the right-handed Dehn twist, and in particular is realized as a diffeomorphism of the surface. We investigate the case where the loop has a single transverse double point, and show that in this case the generalized Dehn twist is not realized as a diffeomorphism.

scholarly journals Classifications of 2-complexes whose finite fundamental group is that of a 3-manifold

1997 ◽  
Vol 40 (1) ◽  
pp. 69-84 ◽  
Author(s):  
F. Rudolf Beyl ◽  
M. Paul Latiolais ◽  
Nancy Waller
Keyword(s):  
Fundamental Group ◽  
Euler Characteristic ◽  
Group Ring ◽  
Sufficient Conditions ◽  
Universal Cover ◽  
Homotopy Equivalent ◽  
Spherical Space ◽  
Space Forms ◽  
Simple Homotopy ◽  
Spherical Space Forms

We consider spines of spherical space forms; i.e., spines of closed oriented 3-manifolds whose universal cover is the 3-sphere. We give sufficient conditions for such spines to be homotopy or simple homotopy equivalent to 2-complexes with the same fundamental group G and minimal Euler characteristic 1. If the group ring ℤG satisfies stably-free cancellation, then any such 2-complex is homotopy equivalent to a spine of a 3-manifold. If K1(ℤG) is represented by units and K is homotopy equivalent to a spine X, then K and X are simple homotopy equivalent. We exhibit several infinite families of non-abelian groups G for which these conditions apply.

Good Groups

2021 ◽  
pp. 273-282
Author(s):  
Min Hoon Kim ◽  
Patrick Orson ◽  
JungHwan Park ◽  
Arunima Ray
Keyword(s):  
Fundamental Group ◽  
Cyclic Group ◽  
Finite Groups ◽  
Open Problem ◽  
Embedding Theorem ◽  
Infinite Cyclic Group ◽  
Amenable Groups

Good groups are defined in terms of whether capped gropes of height 1.5 contain certain types of immersed discs. The disc embedding theorem holds for 4-manifolds with good fundamental group. It is proven that the infinite cyclic group and finite groups are good, and that extensions and colimits of good groups are good. This shows that all elementary amenable groups are good. The proofs use grope height raising and contraction, together with an analysis of how fundamental group elements behave under these operations. A central open problem in the study of topological 4-manifolds is to determine precisely which groups are good.

Grope Height Raising and 1-storey Capped Towers

2021 ◽  
pp. 239-252
Author(s):  
Peter Feller ◽  
Mark Powell ◽  
Arunima Ray
Keyword(s):  
Fundamental Group ◽  
Embedding Theorem

‘Grope Height Raising and 1-Storey Capped Towers’ upgrades the capped gropes constructed in the previous chapter to 1-storey capped towers. Grope height raising is a technique that shows that every capped grope of height at least 1.5 can be improved to a capped grope of arbitrary height. The technique is explained in this chapter in detail, and used multiple times in the rest of the proof. The chapter closes by showing how to extend capped gropes to 1-storey capped towers. This crucially uses the hypothesis that the fundamental group is good. It is the single place in the proof of the disc embedding theorem that requires this hypothesis.

Prosodic Impairment Associated With Traumatic Brain Injury

2009 ◽  
Vol 19 (3) ◽  
pp. 97-102
Author(s):  
Billy Irwin
Keyword(s):  
Traumatic Brain Injury ◽  
Brain Injury ◽  
Detailed Analysis ◽  
Acoustic Characteristics ◽  
Individual Variations

Abstract Purpose: This article discusses impaired prosody production subsequent to traumatic brain injury (TBI). Prosody may affect naturalness and intelligibility of speech significantly, often for the long term, and TBI may result in a variety of impairments. Method: Intonation, rate, and stress production are discussed in terms of the perceptual, physiological, and acoustic characteristics associated with TBI. Results and Conclusions: All aspects of prosodic production are susceptible to the effects of damage resulting from TBI. There are commonly associated prosodic impairments; however, individual variations in specific aspects of prosody require detailed analysis.

Assessment of the state and level of development of public-private partnership projects in the subjects of the Russian Federation

2018 ◽  
pp. 131-141 ◽  
Author(s):  
A. N. Savrukov ◽  
N. T. Savrukov ◽  
E. A. Kozlovskaya
Keyword(s):  
Detailed Analysis ◽  
Russian Federation ◽  
Significant Proportion ◽  
Transport Sector ◽  
Private Partnership ◽  
Current State ◽  
Central Regions ◽  
The Russian Federation ◽  
Project Data ◽  
Municipal Level

The article analyzes the current state and level of development of publicprivate partnership (PPP) projects in the subjects of the Russian Federation. The authors conclude that a significant proportion of projects is implemented on a concession basis at the municipal level in the communal sphere. A detailed analysis of the project data showed that the structure of the projects is deformed in favor of the central regions of the Russian Federation, and a significant share in the total amount of financing falls on the transport sector. At the stage of assessing the level of development by the subjects of the Russian Federation, criteria were proposed, and index and integral indicators were used, which ensured comparability of the estimates obtained. At the end of the analysis, the regions were ranked and clustered according to the level of PPP development, which allowed to reveal the number and structure of leaders and outsiders.

To Understand the Informal (on the Book BY V. L. Tambovtsev “Economics of Informal Institutions”)

2015 ◽  
pp. 151-158
Author(s):  
A. Zaostrovtsev
Keyword(s):  
Social Psychology ◽  
Detailed Analysis ◽  
Human Behavior ◽  
Interdisciplinary Approach ◽  
Informal Institutions ◽  
Economic Thought ◽  
History Of ◽  
Original Classification

The review considers the first attempt in the history of Russian economic thought to give a detailed analysis of informal institutions (IF). It recognizes that in general it was successful: the reader gets acquainted with the original classification of institutions (including informal ones) and their genesis. According to the reviewer the best achievement of the author is his interdisciplinary approach to the study of problems and, moreover, his bias on the achievements of social psychology because the model of human behavior in the economic mainstream is rather primitive. The book makes evident that namely this model limits the ability of economists to analyze IF. The reviewer also shares the author’s position that in the analysis of the IF genesis the economists should highlight the uncertainty and reject economic determinism. Further discussion of IF is hardly possible without referring to this book.

The Impact of Property Characteristics on Economic Performance of Russian Industrial Enterprises

2005 ◽  
pp. 53-68 ◽  
Author(s):  
R. Kapeliushnikov ◽  
N. Demina
Keyword(s):  
Detailed Analysis ◽  
Economic Performance ◽  
Ownership Concentration ◽  
Corporate Sector ◽  
Concentrated Ownership ◽  
Industrial Enterprises ◽  
Russian Industry ◽  
Control Premium ◽  
And Performance ◽  
The Impact

The paper provides new survey evidence on effects of concentrated ownership upon investment and performance in Russian industrial enterprises. Authors trace major changes in their ownership profile, assess pace of post-privatization redistribution of shareholdings and provide evidence on ownership concentration in the Russian industry. The major econometric findings are that the first largest shareholding is negatively associated with the firm’s investment and performance but surprisingly the second largest shareholding is positively associated with them. Moreover, these relationships do not depend on identity of majority shareholders. These results are consistent with the assumption that the entrenched controlling owners are engaged in extracting "control premium" but sizable shareholdings accumulated by other blockholders may put brakes on their expropriating behavior and thus be conductive for efficiency enhancing. The most interesting topic for further more detailed analysis is formation, stability and roles of coalitions of large blockholders in the corporate sector of post-socialist countries.

On the Margins of Modernism

2017 ◽  
Author(s):  
Christopher Rosenmeier
Keyword(s):  
Short Stories ◽  
Detailed Analysis ◽  
Chinese Literature ◽  
Popular Literature ◽  
Extensive Study ◽  
Wide Range ◽  
Chinese Fiction ◽  
Scant Attention ◽  
Narrative Techniques ◽  
Chinese Writing

Xu Xu and Wumingshi were among the most widely read authors in China during and after the Second Sino-Japanese War (1937–1945). Despite being an integral part of the Chinese literary scene, their bestselling fiction has, however, been given scant attention in histories of Chinese writing. This book is the first extensive study of Xu Xu and Wumingshi in English or any other Western language and it re-establishes their importance within the popular Chinese literature of the 1940s. Their romantic novels and short stories were often set abroad and featured a wide range of stereotypes, from pirates, spies and patriotic soldiers to ghosts, spirits and exotic women who confounded the mostly cosmopolitan male protagonists. Christopher Rosenmeier’s detailed analysis of these popular novels and short stories shows that such romances broke new ground by incorporating and adapting narrative techniques and themes from the Shanghai modernist writers of the 1930s, notably Shi Zhecun and Mu Shiying. The study thereby contests the view that modernism had little lasting impact on Chinese fiction, and it demonstrates that the popular literature of the 1940s was more innovative than usually imagined, with authors, such as those studied here, successfully crossing the boundaries between the popular and the elite, as well as between romanticism and modernism, in their bestselling works.

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