scholarly journals Reidemeister–Turaev torsion modulo one of rational homology three-spheres

2003 ◽  
Vol 7 (2) ◽  
pp. 773-787 ◽  
Author(s):  
Florian Deloup ◽  
Gwenael Massuyeau
Keyword(s):  
Rational Homology ◽  
Turaev Torsion

scholarly journals LENS SPACE SURGERIES ALONG CERTAIN 2-COMPONENT LINKS RELATED WITH PARK’S RATIONAL BLOW DOWN, AND REIDEMEISTER-TURAEV TORSION

2013 ◽  
Vol 96 (1) ◽  
pp. 78-126 ◽  
Author(s):  
TERUHISA KADOKAMI ◽  
YUICHI YAMADA
Keyword(s):  
Main Tool ◽  
Lens Space ◽  
The Other ◽  
Dehn Surgery ◽  
Rational Homology ◽  
Blow Down ◽  
Alexander Polynomials ◽  
Other Hand ◽  
Turaev Torsion

AbstractWe study lens space surgeries along two different families of 2-component links, denoted by${A}_{m, n} $and${B}_{p, q} $, related with the rational homology$4$-ball used in J. Park’s (generalized) rational blow down. We determine which coefficient$r$of the knotted component of the link yields a lens space by Dehn surgery. The link${A}_{m, n} $yields a lens space only by the known surgery with$r= mn$and unexpectedly with$r= 7$for$(m, n)= (2, 3)$. On the other hand,${B}_{p, q} $yields a lens space by infinitely many$r$. Our main tool for the proof are the Reidemeister-Turaev torsions, that is, Reidemeister torsions with combinatorial Euler structures. Our results can be extended to the links whose Alexander polynomials are same as those of${A}_{m, n} $and${B}_{p, q} $.

scholarly journals SEIBERG–WITTEN INVARIANTS OF RATIONAL HOMOLOGY 3-SPHERES

2004 ◽  
Vol 06 (06) ◽  
pp. 833-866 ◽  
Author(s):  
LIVIU I. NICOLAESCU
Keyword(s):  
Homology Sphere ◽  
Rational Homology ◽  
Turaev Torsion ◽  
Rational Homology Sphere

We prove that the Seiberg–Witten invariants of a rational homology sphere are determined by the Casson–Walker invariant and the Reidemeister–Turaev torsion.

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 .

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.

scholarly journals Calculus of functors, operad formality, and rational homology of embedding spaces

2007 ◽  
Vol 199 (2) ◽  
pp. 153-198 ◽  
Author(s):  
Gregory Arone ◽  
Pascal Lambrechts ◽  
Ismar Volić
Keyword(s):  
Rational Homology ◽  
Calculus Of Functors ◽  
Embedding Spaces

scholarly journals THE HOMFLY POLYNOMIAL FOR LINKS IN RATIONAL HOMOLOGY 3-SPHERES

Topology ◽  
1999 ◽  
Vol 38 (1) ◽  
pp. 95-115 ◽  
Author(s):  
Efstratia Kalfagianni ◽  
Xiao-Song Lin
Keyword(s):  
Homfly Polynomial ◽  
Rational Homology
Sign in / Sign up

Export Citation Format

Share Document