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Applications of cohomology to questions in set theory i: hausdorff gaps
[article]

1993
*
arXiv
*
pre-print

We explore an

arXiv:math/9311205v1
fatcat:tmwtogf3rzapdmc2w3ol3krfsy
*application**of*homological algebra*to**set*theoretic objects by developing a*cohomology**theory*for*Hausdorff**gaps*. ... The*cohomology**theory*is introduced with enough generality*to*be*applicable**to*other questions in*set**theory*. ... Section 1 Introduction*Hausdorff**gaps*appear in a wide scope*of**applications*in the literature on*set**theory*and a fitting and voluminous tribute*to*the importance*of*these objects has recently been published ...##
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Applications of cohomology to set theory I: Hausdorff gaps

1995
*
Annals of Pure and Applied Logic
*

We explore an

doi:10.1016/0168-0072(94)00020-4
fatcat:fsr3npihsnfd5kh5ewoxp35hku
*application**of*homological algebra*to**set*theoretic objects by developing a*cohomology**theory*for*Hausdorff**gaps*. ... The*cohomology**theory*is introduced with enough generality*to*be*applicable**to*other questions in*set**theory*. ... Introduction*Hausdorff**gaps*appear in a wide scope*of**applications*in the literature on*set**theory*and a fitting and voluminous tribute*to*the importance*of*these objects has recently been published by ...##
###
Pathology in dynamical systems I: General theory

1976
*
Journal of Differential Equations
*

This paper presents definitions

doi:10.1016/0022-0396(76)90018-8
fatcat:qfmrxukuknayzdliogopytzibq
*of*"transversal" and "nondegenerate" which are more readily verified in*applications*, and which still lead*to*topological results on the pathology*of*orbits analogous*to*... Part*I*is done completely without smoothness assumptions. ... The*theory*can also be shown*to*be continuous, and in fact, for compact*Hausdorff*pairs, is identical with the usual Tech*theory*. ...##
###
Spectral Continuity for Aperiodic Quantum Systems I. General Theory
[article]

2018
*
arXiv
*
pre-print

The use

arXiv:1709.00975v2
fatcat:cjspnkubjrfpbphxmqjfujlusq
*of*the*Hausdorff*topology turns out*to*be fundamental in understanding why and how these approximations work. ... In this work a positive answer is provided using the rather general*setting**of*groupoid C^∗-algebras. ... Some*of*these results are slightly extended*to*cover all potential*applications*. ...##
###
Twisted index theory on good orbifolds, I: noncommutative Bloch theory
[article]

1999
*
arXiv
*
pre-print

In Part

arXiv:math/9911102v1
fatcat:v55y5mgn5jaipdkjd5cfxq5n74
*I*we study the twisted index*theory**of*elliptic operators on orbifold covering spaces*of*compact good orbifolds, which are invariant under a projective action*of*the orbifold fundamental group. ... We apply these results*to*obtain qualitative results on real and complex hyperbolic spaces in 2 and 4 dimensions, related*to*generalizations*of*the Bethe-Sommerfeld conjecture and the Ten Martini Problem ... More precisely, an orbifold M*of*dimension m is a*Hausdorff*, second countable topological space with a Satake atlas V = {U*i*, φ*i*} which covers M , consisting*of*open*sets*U*i*and homeomorphisms φ*i*...##
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Page 8840 of Mathematical Reviews Vol. , Issue 2002M
[page]

2002
*
Mathematical Reviews
*

Denoting by £; the

*set**of*reals where the asymptotic frequency*of*some digit in the f-expansion differs by at least 6 from the frequency prescribed by wv, they prove that E; has*Hausdorff*dimension less ... certain*applications*.” ...##
###
Page 638 of Mathematical Reviews Vol. , Issue 85b
[page]

1985
*
Mathematical Reviews
*

*theory*provides

*cohomology*

*theories*for these categories as well. ... It seems still

*to*be open whether the

*gap*between cmp X amd def X can be arbitrarily large. ...

##
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Page 5887 of Mathematical Reviews Vol. , Issue 90J
[page]

1990
*
Mathematical Reviews
*

Kalnins (NZ-WAIK)
90j:58119 58F19 14K20 35P99 35Q20 47F0S 58G25
Krichever,

*I*. M. (2-MPI) Spectral*theory**of*two-dimensional periodic operators and its*applications*. (Russian) Uspekhi Mat. ... Each cross section*to*the suspension flow is dual*to*a*cohomology*class and each*of*these*cohomology*classes determines an infinite cyclic cover*of*M. ...##
###
Three-manifolds, Foliations and Circles, I
[article]

1997
*
arXiv
*
pre-print

The skew R-covered Anosov foliations

arXiv:math/9712268v1
fatcat:uiozlkod2rbcxhlz34wsqcdlse
*of*Sergio Fenley are examples. We hope later*to*use this structure for geometrization*of*slithered 3-manifolds. ... We show that all such foliations admit transverse pseudo-Anosov flows, and that in the universal cover*of*the hyperbolic cases, the leaves limit*to*sphere-filling Peano curves. ... Then J ∩*I*ν is a Cantor*set*, since*gaps*are dense and there are no atoms*to*L + (ν). ...##
###
Book Review: Lie theory and special functions

1969
*
Bulletin of the American Mathematical Society
*

Rectifiable

doi:10.1090/s0002-9904-1969-12292-5
fatcat:c4vvcmogs5dw7pdctczubgqdra
*sets*have become objects*of*fundamental importance*to*measure theoretic geometry since they are essential in describing the structure*of**sets**of*finite ^-dimensional*Hausdorff*measure. ... The irreducible representations*of*the associate Lie algebra are obtained but, because*of*computational difficulties, detailed*applications*are omitted. We expect this*gap**to*be filled in the future. ...##
###
Relating Diffraction and Spectral Data of Aperiodic Tilings: Towards a Bloch theorem
[article]

2020
*
arXiv
*
pre-print

properties (

arXiv:2007.15961v1
fatcat:6wkmi3apajhibii2zv73l46fvi
*of*Hamiltonians defined on such tilings) defined by K-*theory*, and*to*show their equivalence in dimensions ≤ 3. ... The purpose*of*this paper is*to*show the relationship in all dimensions between the structural (diffraction pattern) aspect*of*tilings (described by Čech*cohomology**of*the tiling space) and the spectral ... The transversal N in our*applications*is a Cantor*set*, zero-dimensional, so its*cohomology*vanishes in positive dimensions. ...##
###
Equivariant Cartan-Eilenberg supergerbes for the Green-Schwarz superbranes I. The super-Minkowskian case
[article]

2020
*
arXiv
*
pre-print

*cohomology*

*of*its Lie superalgebra, the

*gap*between the two

*cohomologies*being bridged by a super-variant

*of*the classic Chevalley-Eilenberg construction. ... straightforward identification

*of*the supergeometric mechanisms and unobstructed development

*of*formal tools

*to*be employed in more complex circumstances. ... [Mur96, MS00, Ste00, BCM+02, CJM02, CJM+05] -ample structural

*applications*in the study

*of*σ-models and the associated conformal field

*theories*and string

*theories*, and in particular in a neat

*cohomological*...

##
###
A spectral sequence for the K-theory of tiling spaces

2009
*
Ergodic Theory and Dynamical Systems
*

. , e d } is the canonical basis

doi:10.1017/s0143385708000539
fatcat:zk2zaxzlznchzkxa2y7ypv7moi
*of*Z d , α*i*= α e*i*is the restriction*of*α*to*the ith component*of*Z d , whereas x∧ is the exterior multiplication by x ∈ Z d . ... There is a spectral sequence converging*to*the K -*theory**of*A E r s 2 ⇒ K r +s+d (A α Z d ), with page-2 isomorphic*to*the*cohomology**of*the PV complex. † J.B. is indebted*to*M. ... (for*cohomology*or K -*theory*in particular). ...##
###
Page 389 of Mathematical Reviews Vol. 56, Issue 2
[page]

1978
*
Mathematical Reviews
*

The independence

*of*the results from Zermelo- Frankel*set**theory*remains open. Paul C. Eklof (Irvine, Calif.) Manin, Ju.*I*. 2821 The continuum problem. ... ., 1971] tried*to*prove that the assumption | A?=A was equivalent*to*being a homomorphic image*of*a Suslin algebra*of**sets*(with the real operation A), but there was a*gap*. ...##
###
Page 2271 of Mathematical Reviews Vol. , Issue 2004c
[page]

2004
*
Mathematical Reviews
*

*To*do this, he starts by introducing a number

*of*equivalence relations, most on the “

*set*”

*of*all met- ric spaces—among them coarse equivalence, Gromov-

*Hausdorff*equivalence, Lipschitz (homotopy) equivalence ... Part

*I*

*of*the paper under review is devoted

*to*equivari- ant elliptic

*cohomology*with respect

*to*a finite group G

*of*odd order n and an elliptic curve Eyniy given by y? ...

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