Split-Hopf fibrations

2021 ◽  
Author(s):  
Craig Nolder ◽  
Benjamin Prather
Keyword(s):  
Hopf Fibrations

scholarly journals Cyclic-Homology Chern–Weil Theory for Families of Principal Coactions

2020 ◽  
Author(s):  
Piotr M. Hajac ◽  
Tomasz Maszczyk
Keyword(s):  
Cyclic Homology ◽  
Quantum Deformation ◽  
Homotopy Formula ◽  
Standard Quantum ◽  
Unital Algebra ◽  
Hopf Fibrations ◽  
Chain Homotopy ◽  
Cartan Model ◽  
Extension Algebra ◽  
Hochschild Complex

AbstractViewing the space of cotraces in the structural coalgebra of a principal coaction as a noncommutative counterpart of the classical Cartan model, we construct the cyclic-homology Chern–Weil homomorphism. To realize the thus constructed Chern–Weil homomorphism as a Cartan model of the homomorphism tautologically induced by the classifying map on cohomology, we replace the unital subalgebra of coaction-invariants by its natural H-unital nilpotent extension (row extension). Although the row-extension algebra provides a drastically different model of the cyclic object, we prove that, for any row extension of any unital algebra over a commutative ring, the row-extension Hochschild complex and the usual Hochschild complex are chain homotopy equivalent. It is the discovery of an explicit homotopy formula that allows us to improve the homological quasi-isomorphism arguments of Loday and Wodzicki. We work with families of principal coactions, and instantiate our noncommutative Chern–Weil theory by computing the cotrace space and analyzing a dimension-drop-like effect in the spirit of Feng and Tsygan for the quantum-deformation family of the standard quantum Hopf fibrations.

scholarly journals Random Holonomy for Hopf Fibrations

2001 ◽  
Vol 182 (2) ◽  
pp. 371-389 ◽  
Author(s):  
Robert O. Bauer ◽  
Eric A. Carlen
Keyword(s):  
Hopf Fibrations

scholarly journals Chern numbers for two families of noncommutative Hopf fibrations

2003 ◽  
Vol 336 (11) ◽  
pp. 925-930 ◽  
Author(s):  
Piotr M. Hajac ◽  
Rainer Matthes ◽  
Wojciech Szymański
Keyword(s):  
Hopf Fibrations ◽  
Chern Numbers

Diffeomorphisms taking lines to circles, and quaternionic Hopf fibrations

2006 ◽  
Vol 40 (2) ◽  
pp. 108-116 ◽  
Author(s):  
V. A. Timorin
Keyword(s):  
Hopf Fibrations

scholarly journals Linking pairing and Hopf fibrations on $S^{3}$

2015 ◽  
Vol 67 (1) ◽  
pp. 419-432
Author(s):  
Noboru OGAWA
Keyword(s):  
Hopf Fibrations

scholarly journals From Hopf fibrations to exotic causal replacements

2016 ◽  
Vol 94 (8) ◽  
Author(s):  
Miguel Bezares ◽  
Érico Goulart ◽  
Gonzalo Palomera ◽  
Daniel J. Pons ◽  
Enrique G. Reyes
Keyword(s):  
Hopf Fibrations

scholarly journals On the Relationship between Classical and Deformed Hopf Fibrations

2020 ◽  
Author(s):  
Tomasz Brzeziński ◽  
◽  
James Gaunt ◽  
Alexander Schenkel ◽  
◽  
...  
Keyword(s):  
Hopf Fibrations ◽  
The Relationship

Discrete Hopf Fibrations in the Signal Space of Four-Dimensional Modulations

2017 ◽  
Author(s):  
Fernando Alves Rodrigues ◽  
Guilherme Penello Temporão ◽  
Jean Pierre von der Weid
Keyword(s):  
Signal Space ◽  
Hopf Fibrations
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