scholarly journals Spaces with Noetherian cohomology

2012 ◽  
Vol 56 (1) ◽  
pp. 13-25
Author(s):  
Kasper K. S. Andersen ◽  
Natàlia Castellana ◽  
Vincent Franjou ◽  
Alain Jeanneret ◽  
Jérôme Scherer
Keyword(s):  
Fundamental Group ◽  
Compact Group ◽  
Compact Groups ◽  
Classifying Space ◽  
Noetherian Module

AbstractIs the cohomology of the classifying space of a p-compact group, with Noetherian twisted coefficients, a Noetherian module? In this paper we provide, over the ring of p-adic integers, such a generalization to p-compact groups of the Evens–Venkov Theorem. We consider the cohomology of a space with coefficients in a module, and we compare Noetherianity over the field with p elements with Noetherianity over the p-adic integers, in the case when the fundamental group is a finite p-group.

scholarly journals Compact groups with a set of positive Haar measure satisfying a nilpotent law

2021 ◽  
pp. 1-4
Author(s):  
ALIREZA ABDOLLAHI ◽  
MEISAM SOLEIMANI MALEKAN
Keyword(s):  
Compact Group ◽  
Haar Measure ◽  
Positive Answer ◽  
Nilpotent Subgroup ◽  
Compact Groups

Abstract The following question is proposed by Martino, Tointon, Valiunas and Ventura in [4, question 1·20]: Let G be a compact group, and suppose that \[\mathcal{N}_k(G) = \{(x_1,\dots,x_{k+1}) \in G^{k+1} \;|\; [x_1,\dots, x_{k+1}] = 1\}\] has positive Haar measure in $G^{k+1}$ . Does G have an open k-step nilpotent subgroup? We give a positive answer for $k = 2$ .

scholarly journals Ends of locally compact groups and their coset spaces

1974 ◽  
Vol 17 (3) ◽  
pp. 274-284 ◽  
Author(s):  
C. H. Houghton
Keyword(s):  
Compact Group ◽  
Direct Product ◽  
Compact Space ◽  
Locally Compact Group ◽  
Locally Compact Groups ◽  
Compact Groups ◽  
Countable Base ◽  
Locally Compact ◽  
Coset Spaces ◽  
Compact Boundary

Freudenthal [5, 7] defined a compactification of a rim-compact space, that is, a space having a base of open sets with compact boundary. The additional points are called ends and Freudenthal showed that a connected locally compact non-compact group having a countable base has one or two ends. Later, Freudenthal [8], Zippin [16], and Iwasawa [11] showed that a connected locally compact group has two ends if and only if it is the direct product of a compact group and the reals.

scholarly journals A note on the duality of locally compact groups

1968 ◽  
Vol 9 (2) ◽  
pp. 87-91 ◽  
Author(s):  
J. W. Baker
Keyword(s):  
Abelian Group ◽  
Compact Group ◽  
Locally Compact Group ◽  
Locally Compact Groups ◽  
Compact Groups ◽  
Group Topology ◽  
Locally Compact ◽  
Natural Way

Let H be a group of characters on an (algebraic) abelian group G. In a natural way, we may regard G as a group of characters on H. In this way, we obtain a duality between the two groups G and H. One may pose several problems about this duality. Firstly, one may ask whether there exists a group topology on G for which H is precisely the set of continuous characters. This question has been answered in the affirmative in [1]. We shall say that such a topology is compatible with the duality between G and H. Next, one may ask whether there exists a locally compact group topology on G which is compatible with a given duality and, if so, whether there is more than one such topology. It is this second question (previously considered by other authors, to whom we shall refer below) which we shall consider here.

scholarly journals Rudin-Shapiro sequences for arbitrary compact groups

1976 ◽  
Vol 22 (4) ◽  
pp. 421-430 ◽  
Author(s):  
J. R. McMullen ◽  
J. F. Price
Keyword(s):  
Compact Group ◽  
Trigonometric Polynomials ◽  
Compact Groups ◽  
Group A ◽  
Image Position

AbstractLet G be a compact group. A sequence of functions in L∞ (G) is said to be a Rudin-Shapiro sequence (briefly, an RS-sequence) if the following conditions hold: (1) (2) (3) The main purpose here is to prove the following theorem: Theorem: Theorem. Let G be an infinite compact group. Then G has an RS-sequence consisting of trigonometric polynomials.

scholarly journals Photometry of Hickson Compact Group N.90

1994 ◽  
Vol 161 ◽  
pp. 619-622
Author(s):  
G. Longo ◽  
H. Lorenz ◽  
G. Richter ◽  
G. Busarello
Keyword(s):  
Compact Group ◽  
Compact Groups ◽  
Ccd Photometry ◽  
Groups Of Galaxies

Deep CCD photometry and kinematical observations can be used to constrain the dynamical status of compact groups of galaxies. In the case of Hickson 90 the main interaction is taking place between NGC 7174 and NGC 7173 while NGC 7176 appears to be virtually undisturbed.

scholarly journals Mass Distribution in Compact Groups

2000 ◽  
Vol 174 ◽  
pp. 377-380 ◽  
Author(s):  
J. Perea ◽  
A. del Olmo ◽  
L. Verdes-Montenegro ◽  
M. S. Yun ◽  
W.K. Huchtmeier ◽  
...  
Keyword(s):  
Compact Group ◽  
Mass Distribution ◽  
Spiral Galaxies ◽  
Main Group ◽  
Stable System ◽  
Compact Groups ◽  
Dark Halo ◽  
Potential Well ◽  
Redshift Surveys ◽  
Satellite Galaxies

AbstractNew redshift surveys of galaxies in the field of compact groups have discovered a population of faint galaxies which act as satellites orbiting in the potential well of the bright group. Here we analyze the mass distribution of the groups by comparing the mass derived from the bright members and the mass obtained from the satellite galaxies. Our analysis indicates the presence of a dark halo around the main group with a mass roughly four times that measured for the dominant galaxies of the compact group.We found that heavier halos are ruled out by the observations when comparing the distribution of positions and redshifts of the satellite galaxies with the distribution of satellites of isolated spiral galaxies. The results agree with a picture where compact groups may form a stable system with galaxies moving in a common dark halo.

scholarly journals On Analytic Todd Classes of Singular Varieties

2019 ◽  
Author(s):  
Francesco Bei ◽  
Paolo Piazza
Keyword(s):  
Fundamental Group ◽  
Complex Space ◽  
Homology Class ◽  
Classifying Space ◽  
Projective Varieties ◽  
Singular Varieties ◽  
Push Forward ◽  
Birational Invariant ◽  
Complex Projective

Abstract Let $(X,h)$ be a compact and irreducible Hermitian complex space. This paper is devoted to various questions concerning the analytic K-homology of $(X,h)$. In the 1st part, assuming either $\dim (\operatorname{sing}(X))=0$ or $\dim (X)=2$, we show that the rolled-up operator of the minimal $L^2$-$\overline{\partial }$ complex, denoted here $\overline{\eth }_{\textrm{rel}}$, induces a class in $K_0 (X)\equiv KK_0(C(X),\mathbb{C})$. A similar result, assuming $\dim (\operatorname{sing}(X))=0$, is proved also for $\overline{\eth }_{\textrm{abs}}$, the rolled-up operator of the maximal $L^2$-$\overline{\partial }$ complex. We then show that when $\dim (\operatorname{sing}(X))=0$ we have $[\overline{\eth }_{\textrm{rel}}]=\pi _*[\overline{\eth }_M]$ with $\pi :M\rightarrow X$ an arbitrary resolution and with $[\overline{\eth }_M]\in K_0 (M)$ the analytic K-homology class induced by $\overline{\partial }+\overline{\partial }^t$ on $M$. In the 2nd part of the paper we focus on complex projective varieties $(V,h)$ endowed with the Fubini–Study metric. First, assuming $\dim (V)\leq 2$, we compare the Baum–Fulton–MacPherson K-homology class of $V$ with the class defined analytically through the rolled-up operator of any $L^2$-$\overline{\partial }$ complex. We show that there is no $L^2$-$\overline{\partial }$ complex on $(\operatorname{reg}(V),h)$ whose rolled-up operator induces a K-homology class that equals the Baum–Fulton–MacPherson class. Finally in the last part of the paper we prove that under suitable assumptions on $V$ the push-forward of $[\overline{\eth }_{\textrm{rel}}]$ in the K-homology of the classifying space of the fundamental group of $V$ is a birational invariant.

A decomposition theorem for locally compact groups

2019 ◽  
Vol 26 (1) ◽  
pp. 29-33
Author(s):  
Sanjib Basu ◽  
Krishnendu Dutta
Keyword(s):  
Compact Group ◽  
Lebesgue Point ◽  
Decomposition Theorem ◽  
Locally Compact Group ◽  
The Other ◽  
Locally Compact Groups ◽  
Compact Groups ◽  
Topological Groups ◽  
Locally Compact ◽  
Interesting Connection

Abstract We prove that, under certain restrictions, every locally compact group equipped with a nonzero, σ-finite, regular left Haar measure can be decomposed into two small sets, one of which is small in the sense of measure and the other is small in the sense of category, and all such decompositions originate from a generalised notion of a Lebesgue point. Incidentally, such class of topological groups for which this happens turns out to be metrisable. We also observe an interesting connection between Luzin sets in such spaces and decompositions of the above type.

scholarly journals Nonmeasurable subgroups of compact groups

2016 ◽  
Vol 19 (1) ◽  
Author(s):  
Salvador Hernández ◽  
Karl H. Hofmann ◽  
Sidney A. Morris
Keyword(s):  
Compact Group ◽  
Borel Subgroup ◽  
Affirmative Answer ◽  
Compact Groups ◽  
Profinite Groups

AbstractIn 1985 S. Saeki and K. Stromberg published the following question: Does every infinite compact group have a subgroup which is not Haar measurable? An affirmative answer is given for all compact groups with the exception of some metric profinite groups which are almost perfect and strongly complete. In this spirit it is also shown that every compact group contains a non-Borel subgroup.

scholarly journals Some remarks on representations up to homotopy

2016 ◽  
Vol 13 (03) ◽  
pp. 1650024
Author(s):  
Giorgio Trentinaglia ◽  
Chenchang Zhu
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Compact Group ◽  
Compact Groups ◽  
Quantum Field ◽  
Algebraic Quantum Field Theory ◽  
Trivial Bundle ◽  
Finite Dimensional ◽  
Algebraic Quantum

Motivated by the study of the interrelation between functorial and algebraic quantum field theory (AQFT), we point out that on any locally trivial bundle of compact groups, representations up to homotopy are enough to separate points by means of the associated representations in cohomology. Furthermore, we observe that the derived representation category of any compact group is equivalent to the category of ordinary (finite-dimensional) representations of the group.

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