First Singular Homology Group of Spacetime

2019 ◽  
Vol 84 (2) ◽  
pp. 245-252
Author(s):  
Gunjan Agrawal ◽  
Roma Pathak
Keyword(s):  
Homology Group ◽  
Singular Homology

Singular homology theory in the category of soft topological spaces

2015 ◽  
Vol 22 (4) ◽  
Author(s):  
Sadi Bayramov ◽  
Cigdem Gündüz (Aras) ◽  
Leonard Mdzinarishvili
Keyword(s):  
Homology Group ◽  
Homology Theory ◽  
Topological Spaces ◽  
Homology Groups ◽  
Relative Homology ◽  
Singular Homology

AbstractIn the category of soft topological spaces, a singular homology group is defined and the homotopic invariance of this group is proved [Internat. J. Engrg. Innovative Tech. (IJEIT) 3 (2013), no. 2, 292–299]. The first aim of this study is to define relative homology groups in the category of pairs of soft topological spaces. For these groups it is proved that the axioms of dimensional and exactness homological sequences hold true. The axiom of excision for singular homology groups is also proved.

scholarly journals A Birman exact sequence for the Torelli subgroup of Aut(Fn)

2016 ◽  
Vol 26 (03) ◽  
pp. 585-617 ◽  
Author(s):  
Matthew Day ◽  
Andrew Putman
Keyword(s):  
Exact Sequence ◽  
Recent Work ◽  
Homology Group ◽  
Entire Group ◽  
Torelli Group

We develop an analogue of the Birman exact sequence for the Torelli subgroup of [Formula: see text]. This builds on earlier work of the authors, who studied an analogue of the Birman exact sequence for the entire group [Formula: see text]. These results play an important role in the authors’ recent work on the second homology group of the Torelli group.

scholarly journals One-relator groups and algebras related to polyhedral products

2021 ◽  
pp. 1-20
Author(s):  
Jelena Grbić ◽  
George Simmons ◽  
Marina Ilyasova ◽  
Taras Panov
Keyword(s):  
Homology Group ◽  
Homotopy Theory ◽  
Commutator Subgroup ◽  
Homology Groups ◽  
Homological Characterization ◽  
One Relator Groups ◽  
Combinatorial Condition ◽  
The Moment ◽  
Necessary And Sufficient

We link distinct concepts of geometric group theory and homotopy theory through underlying combinatorics. For a flag simplicial complex $K$ , we specify a necessary and sufficient combinatorial condition for the commutator subgroup $RC_K'$ of a right-angled Coxeter group, viewed as the fundamental group of the real moment-angle complex $\mathcal {R}_K$ , to be a one-relator group; and for the Pontryagin algebra $H_{*}(\Omega \mathcal {Z}_K)$ of the moment-angle complex to be a one-relator algebra. We also give a homological characterization of these properties. For $RC_K'$ , it is given by a condition on the homology group $H_2(\mathcal {R}_K)$ , whereas for $H_{*}(\Omega \mathcal {Z}_K)$ it is stated in terms of the bigrading of the homology groups of $\mathcal {Z}_K$ .

scholarly journals Functorial seminorms on singular homology and (in)flexible manifolds

2015 ◽  
Vol 15 (3) ◽  
pp. 1453-1499 ◽  
Author(s):  
Diarmuid Crowley ◽  
Clara Löh
Keyword(s):  
Singular Homology

On Kähler nilmanifolds with top homology in codimension two

2006 ◽  
Vol 74 (1) ◽  
pp. 85-90
Author(s):  
Bruce Gilligan
Keyword(s):  
Lie Group ◽  
Homology Group ◽  
Discrete Subgroup ◽  
Nilpotent Lie Group ◽  
Codimension Two

SupposeGis a connected, complex, nilpotent Lie group and Γ is a discrete subgroup ofGsuch thatG/Γ is Kähler and the top nonvanishing homology group ofG/Γ (with coefficients in ℤ2) is in codimension two or less. We show thatGis then Abelian. We also note that an example from [12] shows that this fails if the top nonvanishing homology is in codimension three.

scholarly journals Computing the fundamental group of a higher-rank graph

2021 ◽  
pp. 1-12
Author(s):  
Sooran Kang ◽  
David Pask ◽  
Samuel B.G. Webster
Keyword(s):  
Fundamental Group ◽  
Homology Group ◽  
Klein Bottle ◽  
Fundamental Groups ◽  
The Third ◽  
Higher Rank ◽  
The One ◽  
Standard Presentation

Abstract We compute a presentation of the fundamental group of a higher-rank graph using a coloured graph description of higher-rank graphs developed by the third author. We compute the fundamental groups of several examples from the literature. Our results fit naturally into the suite of known geometrical results about higher-rank graphs when we show that the abelianization of the fundamental group is the homology group. We end with a calculation which gives a non-standard presentation of the fundamental group of the Klein bottle to the one normally found in the literature.

scholarly journals An example of anomalous singular homology

1962 ◽  
Vol 13 (2) ◽  
pp. 293-293 ◽  
Author(s):  
M. G. Barratt ◽  
John Milnor
Keyword(s):  
Singular Homology

scholarly journals Existence of Taut Foliations on Seifert Fibered Homology 3-spheres

2014 ◽  
Vol 66 (1) ◽  
pp. 141-169
Author(s):  
Shanti Caillat-Gibert ◽  
Daniel Matignon
Keyword(s):  
Homology Group ◽  
Integral Homology

AbstractThis paper concerns the problem of existence of taut foliations among 3-manifolds. From the work of David Gabai we know that a closed 3-manifold with non-trivial second homology group admits a taut foliation. The essential part of this paper focuses on Seifert fibered homology 3-spheres. The result is quite different if they are integral or rational but non-integral homology 3-spheres. Concerning integral homology 3-spheres, we can see that all but the 3-sphere and the Poincaré 3-sphere admit a taut foliation. Concerning non-integral homology 3-spheres, we prove there are infinitely many that admit a taut foliation, and infinitely many without a taut foliation. Moreover, we show that the geometries do not determine the existence of taut foliations on non-integral Seifert fibered homology 3-spheres.

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