scholarly journals Higher simple structure sets of lens spaces with the fundamental group of arbitrary order

2019 ◽  
pp. 267-280
Author(s):  
L’udovít Balko ◽  
Tibor Macko ◽  
Martin Niepel ◽  
Tomáš Rusin
Keyword(s):  
Fundamental Group ◽  
Simple Structure ◽  
Arbitrary Order ◽  
Lens Spaces

Higher simple structure sets of lens spaces with the fundamental group of order 2

2019 ◽  
Vol 263 ◽  
pp. 299-320
Author(s):  
L'udovít Balko ◽  
Tibor Macko ◽  
Martin Niepel ◽  
Tomáš Rusin
Keyword(s):  
Fundamental Group ◽  
Simple Structure ◽  
Lens Spaces

scholarly journals An explicit relation between knot groups in lens spaces and those in S3

2018 ◽  
Vol 27 (08) ◽  
pp. 1850045
Author(s):  
Yuta Nozaki
Keyword(s):  
Fundamental Group ◽  
Lens Space ◽  
Lens Spaces ◽  
Alternative Proof ◽  
Cyclic Covering ◽  
Covering Map ◽  
Explicit Relation

For a cyclic covering map [Formula: see text] between two pairs of a 3-manifold and a knot each, we describe the fundamental group [Formula: see text] in terms of [Formula: see text]. As a consequence, we give an alternative proof for the fact that certain knots in [Formula: see text] cannot be represented as the preimage of any knot in a lens space, which is related to free periods of knots. In our proofs, the subgroup of a group [Formula: see text] generated by the commutators and the [Formula: see text]th power of each element of [Formula: see text] plays a key role.

scholarly journals THE ALEXANDER POLYNOMIAL OF (1,1)-KNOTS

2006 ◽  
Vol 15 (09) ◽  
pp. 1119-1129 ◽  
Author(s):  
A. CATTABRIGA
Keyword(s):  
Fundamental Group ◽  
Alexander Polynomial ◽  
Lens Spaces ◽  
Cyclic Covering ◽  
Genus One

In this paper we investigate the Alexander polynomial of (1,1)-knots, which are knots lying in a 3-manifold with genus one at most, admitting a particular decomposition. More precisely, we study the connections between the Alexander polynomial and a polynomial associated to a cyclic presentation of the fundamental group of an n-fold strongly-cyclic covering branched over the knot K, which we call the n-cyclic polynomial of K. In this way, we generalize to all (1,1)-knots, with the only exception of those lying in S2×S1, a result obtained by Minkus for 2-bridge knots and extended by the author and M. Mulazzani to the case of (1,1)-knots in S3. As corollaries some properties of the Alexander polynomial of knots in S3 are extended to the case of (1,1)-knots in lens spaces.

scholarly journals On fake lens spaces with fundamental group of order a power of 2

2009 ◽  
Vol 9 (3) ◽  
pp. 1837-1883 ◽  
Author(s):  
Tibor Macko ◽  
Christian Wegner
Keyword(s):  
Fundamental Group ◽  
Lens Spaces

A Comparison of Simple Structure Rotation Criteria in Temporal Exploratory Factor Analysis for Event-Related Potential Data

Methodology ◽  
2019 ◽  
Vol 15 (Supplement 1) ◽  
pp. 43-60 ◽  
Author(s):  
Florian Scharf ◽  
Steffen Nestler
Keyword(s):  
Factor Analysis ◽  
Exploratory Factor Analysis ◽  
Simple Structure ◽  
Ground Truth ◽  
Event Related Potential ◽  
Suitable Alternative ◽  
Factor Rotation ◽  
Rotation Methods ◽  
Simple Structure Rotation ◽  
Temporal Overlap

Abstract. It is challenging to apply exploratory factor analysis (EFA) to event-related potential (ERP) data because such data are characterized by substantial temporal overlap (i.e., large cross-loadings) between the factors, and, because researchers are typically interested in the results of subsequent analyses (e.g., experimental condition effects on the level of the factor scores). In this context, relatively small deviations in the estimated factor solution from the unknown ground truth may result in substantially biased estimates of condition effects (rotation bias). Thus, in order to apply EFA to ERP data researchers need rotation methods that are able to both recover perfect simple structure where it exists and to tolerate substantial cross-loadings between the factors where appropriate. We had two aims in the present paper. First, to extend previous research, we wanted to better understand the behavior of the rotation bias for typical ERP data. To this end, we compared the performance of a variety of factor rotation methods under conditions of varying amounts of temporal overlap between the factors. Second, we wanted to investigate whether the recently proposed component loss rotation is better able to decrease the bias than traditional simple structure rotation. The results showed that no single rotation method was generally superior across all conditions. Component loss rotation showed the best all-round performance across the investigated conditions. We conclude that Component loss rotation is a suitable alternative to simple structure rotation. We discuss this result in the light of recently proposed sparse factor analysis approaches.

Filling words in fundamental groups of Riemann surfaces

2013 ◽  
Vol 50 (1) ◽  
pp. 31-50
Author(s):  
C. Zhang
Keyword(s):  
Riemann Surface ◽  
Fundamental Group ◽  
Riemann Surfaces ◽  
Fundamental Groups ◽  
Closed Geodesics ◽  
New Words

The purpose of this article is to utilize some exiting words in the fundamental group of a Riemann surface to acquire new words that are represented by filling closed geodesics.

Representations of the fundamental group and the torsor of deformations. Global aspects

2017 ◽  
Author(s):  
Ahmed Abbes ◽  
Michel Gros
Keyword(s):  
Fundamental Group ◽  
Koszul Complex ◽  
Finiteness Conditions ◽  
Inverse Systems ◽  
Logarithmic Geometry

This chapter continues the construction and study of the p-adic Simpson correspondence and presents the global aspects of the theory of representations of the fundamental group and the torsor of deformations. After fixing the notation and general conventions, the chapter develops preliminaries and then introduces the results and complements on the notion of locally irreducible schemes. It also fixes the logarithmic geometry setting of the constructions and considers a number of results on the Koszul complex. Finally, it develops the formalism of additive categories up to isogeny and describes the inverse systems of a Faltings ringed topos, with a particular focus on the notion of adic modules and the finiteness conditions adapted to this setting. The chapter rounds up the discussion with sections on Higgs–Tate algebras and Dolbeault modules.

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