scholarly journals Gompf connected sum for orbifolds and K-contact Smale–Barden manifolds

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Vicente Muñoz
Keyword(s):  
Rational Homology ◽  
Connected Sum ◽  
Topological Constraints

Abstract We develop the Gompf fiber connected sum operation for symplectic orbifolds. We use it to construct a symplectic 4-orbifold with b 1 = 0 {b_{1}=0} and containing symplectic surfaces of genus 1 and 2 that are disjoint and span the rational homology. This is used in turn to construct a K-contact Smale–Barden manifold with specified 2-homology that satisfies the known topological constraints with sharper estimates than the examples constructed previously. The manifold can be chosen spin or non-spin.

scholarly journals Rational cobordisms and integral homology

2020 ◽  
Vol 156 (9) ◽  
pp. 1825-1845
Author(s):  
Paolo Aceto ◽  
Daniele Celoria ◽  
JungHwan Park
Keyword(s):  
Homology Group ◽  
Floer Homology ◽  
Lens Spaces ◽  
Integral Homology ◽  
Rational Homology ◽  
Cobordism Class ◽  
Connected Sum ◽  
Knot Floer Homology ◽  
Infinite Rank ◽  
Homology Cobordism

We consider the question of when a rational homology $3$-sphere is rational homology cobordant to a connected sum of lens spaces. We prove that every rational homology cobordism class in the subgroup generated by lens spaces is represented by a unique connected sum of lens spaces whose first homology group injects in the first homology group of any other element in the same class. As a first consequence, we show that several natural maps to the rational homology cobordism group have infinite-rank cokernels. Further consequences include a divisibility condition between the determinants of a connected sum of $2$-bridge knots and any other knot in the same concordance class. Lastly, we use knot Floer homology combined with our main result to obstruct Dehn surgeries on knots from being rationally cobordant to lens spaces.

scholarly journals ModularBoost: an efficient network inference algorithm based on module decomposition

2021 ◽  
Vol 22 (1) ◽  
Author(s):  
Xinyu Li ◽  
Wei Zhang ◽  
Jianming Zhang ◽  
Guang Li
Keyword(s):  
Network Inference ◽  
Detection Methods ◽  
Inference Problem ◽  
Topological Constraints ◽  
Inference Algorithms ◽  
Module Detection ◽  
Series Expression ◽  
Gene Modules ◽  
Inference Methods ◽  
Complicated Task

Abstract Background Given expression data, gene regulatory network(GRN) inference approaches try to determine regulatory relations. However, current inference methods ignore the inherent topological characters of GRN to some extent, leading to structures that lack clear biological explanation. To increase the biophysical meanings of inferred networks, this study performed data-driven module detection before network inference. Gene modules were identified by decomposition-based methods. Results ICA-decomposition based module detection methods have been used to detect functional modules directly from transcriptomic data. Experiments about time-series expression, curated and scRNA-seq datasets suggested that the advantages of the proposed ModularBoost method over established methods, especially in the efficiency and accuracy. For scRNA-seq datasets, the ModularBoost method outperformed other candidate inference algorithms. Conclusions As a complicated task, GRN inference can be decomposed into several tasks of reduced complexity. Using identified gene modules as topological constraints, the initial inference problem can be accomplished by inferring intra-modular and inter-modular interactions respectively. Experimental outcomes suggest that the proposed ModularBoost method can improve the accuracy and efficiency of inference algorithms by introducing topological constraints.

Euler classes of vector bundles over manifolds

2021 ◽  
Vol 71 (1) ◽  
pp. 199-210
Author(s):  
Aniruddha C. Naolekar
Keyword(s):  
Vector Bundle ◽  
Vector Bundles ◽  
Euler Class ◽  
Homology Sphere ◽  
Rational Homology ◽  
Rational Homology Sphere ◽  
Orientable Manifolds

Abstract Let 𝓔 k denote the set of diffeomorphism classes of closed connected smooth k-manifolds X with the property that for any oriented vector bundle α over X, the Euler class e(α) = 0. We show that if X ∈ 𝓔2n+1 is orientable, then X is a rational homology sphere and π 1(X) is perfect. We also show that 𝓔8 = ∅ and derive additional cohomlogical restrictions on orientable manifolds in 𝓔 k .

scholarly journals Topological constraints in the reconnection of vortex braids

2021 ◽  
Vol 33 (5) ◽  
pp. 056101
Author(s):  
S. Candelaresi ◽  
G. Hornig ◽  
B. Podger ◽  
D. I. Pontin
Keyword(s):  
Topological Constraints

scholarly journals Effective Action from M-Theory on Twisted Connected Sum G 2-Manifolds

2017 ◽  
Vol 359 (2) ◽  
pp. 535-601 ◽  
Author(s):  
Thaisa C. da C. Guio ◽  
Hans Jockers ◽  
Albrecht Klemm ◽  
Hung-Yu Yeh
Keyword(s):  
Effective Action ◽  
Connected Sum ◽  
M Theory

IWASAWA TYPE FORMULA FOR COVERS OF A LINK IN A RATIONAL HOMOLOGY SPHERE

2008 ◽  
Vol 17 (10) ◽  
pp. 1199-1221 ◽  
Author(s):  
TERUHISA KADOKAMI ◽  
YASUSHI MIZUSAWA
Keyword(s):  
Number Field ◽  
Class Number ◽  
Homology Sphere ◽  
Rational Homology ◽  
Homology Groups ◽  
Cyclic Covers ◽  
Class Number Formula ◽  
Number Formula ◽  
Iwasawa Invariants ◽  
Rational Homology Sphere

Based on the analogy between links and primes, we present an analogue of the Iwasawa's class number formula in a Zp-extension for the p-homology groups of pn-fold cyclic covers of a link in a rational homology 3-sphere. We also describe the associated Iwasawa invariants precisely for some examples and discuss analogies with the number field case.

Aspherical manifolds, Mellin transformation and a question of Bobadilla–Kollár

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Yongqiang Liu ◽  
Laurenţiu Maxim ◽  
Botong Wang
Keyword(s):  
Integral Homology ◽  
Algebraic Varieties ◽  
Finiteness Property ◽  
Rational Homology ◽  
Mellin Transformation ◽  
Hopf Conjecture ◽  
Ball Quotients ◽  
Proper Map ◽  
Complex Projective ◽  
Aspherical Manifolds

Abstract In their paper from 2012, Bobadilla and Kollár studied topological conditions which guarantee that a proper map of complex algebraic varieties is a topological or differentiable fibration. They also asked whether a certain finiteness property on the relative covering space can imply that a proper map is a fibration. In this paper, we answer positively the integral homology version of their question in the case of abelian varieties, and the rational homology version in the case of compact ball quotients. We also propose several conjectures in relation to the Singer–Hopf conjecture in the complex projective setting.

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