scholarly journals Seifert fiber space construction for 𝐺×𝑊

2010 ◽  
pp. 119-137
Author(s):  
Kyung Lee ◽  
Frank Raymond
Keyword(s):  
Fiber Space ◽  
Space Construction ◽  
Seifert Fiber Space

scholarly journals A Survey on Seifert Fiber Space Theorem

ISRN Geometry ◽  
2014 ◽  
Vol 2014 ◽  
pp. 1-9 ◽  
Author(s):  
Jean-Philippe Préaux
Keyword(s):  
Fiber Space ◽  
Seifert Fiber Space ◽  
History Of

We review the history of the proof of the Seifert fiber space theorem, as well as its motivations in 3-manifold topology and its generalizations.

The Seifert Fiber Space Conjecture and Torus Theorem for Nonorientable 3-Manifolds

1994 ◽  
Vol 37 (4) ◽  
pp. 482-489 ◽  
Author(s):  
Wolfgang Heil ◽  
Wilbur Whitten
Keyword(s):  
Normal Subgroup ◽  
Fundamental Group ◽  
Fiber Space ◽  
Seifert Fiber Space

AbstractThe Seifert-fiber-space conjecture for nonorientable 3-manifolds states that if M denotes a compact, irreducible, nonorientable 3-manifold that is not a fake P2 x S1, if π1M is infinite and does not contain Z2 * Z2 as a subgroup, and if π1M does however contain a nontrivial, cyclic, normal subgroup, then M is a Seifert bundle. In this paper, we construct all compact, irreducible, nonorientable 3-manifolds (that do not contain a fake P2 × I) each of whose fundamental group contains Z2 * Z2 and an infinité cyclic, normal subgroup; none of these manifolds admits a Seifert fibration, but they satisfy Thurston's Geometrization Conjecture. We then reformulate the statement of the (nonorientable) SFS-conjecture and obtain a torus theorem for nonorientable manifolds.

RECOGNIZING NONORIENTABLE SEIFERT BUNDLES

1992 ◽  
Vol 01 (04) ◽  
pp. 471-475 ◽  
Author(s):  
WILBUR WHITTEN
Keyword(s):  
Normal Subgroup ◽  
Fundamental Group ◽  
Fiber Space ◽  
Seifert Fiber Space

Roughly speaking, a compact, orientable, irreducible 3-manifold M with infinite fundamental group is a Seifert fiber space, if either 1) π1M contains a nontrivial, cyclic, normal subgroup (the so-called Seifert-fiber-space conjecture), 2) M is finitely covered by a Seifert fiber space, or 3) π1M is isomorphic to the group of a Seifert fiber space. Excluding a fake P2 × S1 where necessary, we show in this paper that similar results hold when M is nonorientable.

scholarly journals Pin(2)-equivariant Seiberg–Witten Floer homology of Seifert fibrations

2019 ◽  
Vol 156 (2) ◽  
pp. 199-250 ◽  
Author(s):  
Matthew Stoffregen
Keyword(s):  
Isomorphism Class ◽  
Floer Homology ◽  
Heegaard Floer Homology ◽  
Homology Sphere ◽  
Integral Homology ◽  
Fiber Space ◽  
Rational Homology ◽  
Seifert Fiber Space ◽  
Homology Cobordism ◽  
Seifert Fiber Spaces

We compute the $\text{Pin}(2)$-equivariant Seiberg–Witten Floer homology of Seifert rational homology three-spheres in terms of their Heegaard Floer homology. As a result of this computation, we prove Manolescu’s conjecture that $\unicode[STIX]{x1D6FD}=-\bar{\unicode[STIX]{x1D707}}$ for Seifert integral homology three-spheres. We show that the Manolescu invariants $\unicode[STIX]{x1D6FC},\unicode[STIX]{x1D6FD},$ and $\unicode[STIX]{x1D6FE}$ give new obstructions to homology cobordisms between Seifert fiber spaces, and that many Seifert homology spheres $\unicode[STIX]{x1D6F4}(a_{1},\ldots ,a_{n})$ are not homology cobordant to any $-\unicode[STIX]{x1D6F4}(b_{1},\ldots ,b_{n})$. We then use the same invariants to give an example of an integral homology sphere not homology cobordant to any Seifert fiber space. We also show that the $\text{Pin}(2)$-equivariant Seiberg–Witten Floer spectrum provides homology cobordism obstructions distinct from $\unicode[STIX]{x1D6FC},\unicode[STIX]{x1D6FD},$ and $\unicode[STIX]{x1D6FE}$. In particular, we identify an $\mathbb{F}[U]$-module called connected Seiberg–Witten Floer homology, whose isomorphism class is a homology cobordism invariant.

Advanced eldercare technology and creative space construction

2014 ◽  
Author(s):  
H.C. Lin ◽  
S.C. Hsu ◽  
Y.H. Huang ◽  
T.C. Yu ◽  
Alice M.K. Wong ◽  
...  
Keyword(s):  
Space Construction ◽  
Creative Space

scholarly journals Generalized almost even-Clifford manifolds and their twistor spaces

2021 ◽  
Vol 8 (1) ◽  
pp. 96-124
Author(s):  
Luis Fernando Hernández-Moguel ◽  
Rafael Herrera
Keyword(s):  
Twistor Space ◽  
Complex Structure ◽  
Twistor Spaces ◽  
Recent Interest ◽  
Generalized Complex Structure ◽  
Generalized Complex ◽  
Space Construction ◽  
Clifford Structures

Abstract Motivated by the recent interest in even-Clifford structures and in generalized complex and quaternionic geometries, we introduce the notion of generalized almost even-Clifford structure. We generalize the Arizmendi-Hadfield twistor space construction on even-Clifford manifolds to this setting and show that such a twistor space admits a generalized complex structure under certain conditions.

scholarly journals Variation of singular Kähler–Einstein metrics: Positive Kodaira dimension

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Junyan Cao ◽  
Henri Guenancia ◽  
Mihai Păun
Keyword(s):  
General Type ◽  
Einstein Metrics ◽  
Kodaira Dimension ◽  
Einstein Metric ◽  
Canonical Bundle ◽  
Fiber Space ◽  
Generic Fiber ◽  
Lelong Numbers ◽  
Kähler Einstein Metrics

Abstract Given a Kähler fiber space p : X → Y {p:X\to Y} whose generic fiber is of general type, we prove that the fiberwise singular Kähler–Einstein metric induces a semipositively curved metric on the relative canonical bundle K X / Y {K_{X/Y}} of p. We also propose a conjectural generalization of this result for relative twisted Kähler–Einstein metrics. Then we show that our conjecture holds true if the Lelong numbers of the twisting current are zero. Finally, we explain the relevance of our conjecture for the study of fiberwise Song–Tian metrics (which represent the analogue of KE metrics for fiber spaces whose generic fiber has positive but not necessarily maximal Kodaira dimension).

scholarly journals Innovative Applications Mode of Network Learning Space in Exercise Physiology Based on Ubiquitous Learning

2019 ◽  
Vol 14 (04) ◽  
pp. 113 ◽  
Author(s):  
Jie Kong
Keyword(s):  
Flipped Classroom ◽  
Exercise Physiology ◽  
Internet Technology ◽  
Traditional Teaching ◽  
Ubiquitous Learning ◽  
Learning Space ◽  
Network Teaching ◽  
Network Learning ◽  
Space Construction

With continuous development of internet technology, the concept of ubiquitous learning and network learning space have received more and more attention from scholars, and gradually become the research focuses. College classroom has turned to network teaching from traditional teaching. In this study, literature review and case study were combined with ubiquitous learning and network learning space construction to systematically discuss classification and concept models of network learning space under the perspective of ubiquitous learning. Meanwhile, four models based on network learning space were proposed, and flipped classroom network teaching model was applied in the course of Exercise Physiology. The study showed that, the model has the good teaching effect in course teaching. It not just improves students’ interest, but also lays a foundation for popularizing the teaching mode.

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