HOMOTOPY FORMULA FOR A LOCAL q -CONCAVE WEDGE IN STEIN MANIFOLDS AND IT’S APPLICATIONS

1998 ◽  
Vol 18 (4) ◽  
pp. 435-439
Author(s):  
Tongde Zhong
Keyword(s):  
Homotopy Formula ◽  
Stein Manifolds

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.

Discs in hulls of real immersions into Stein manifolds

2017 ◽  
Vol 298 (1) ◽  
pp. 334-344
Author(s):  
Rasul Shafikov ◽  
Alexandre Sukhov
Keyword(s):  
Stein Manifolds

scholarly journals TAME DISCRETE SUBSETS IN STEIN MANIFOLDS

2018 ◽  
Vol 107 (1) ◽  
pp. 110-132
Author(s):  
JÖRG WINKELMANN
Keyword(s):  
Lie Groups ◽  
Stein Manifolds

Rosay and Rudin introduced the notion of ‘tameness’ for discrete subsets of $\mathbf{C}^{n}$. We generalize the notion of tameness for discrete sets to arbitrary Stein manifolds, with special emphasis on complex Lie groups.

scholarly journals Cohomology with bounds and Carleman estimates for the∂¯-operator on Stein manifolds

2002 ◽  
Vol 32 (6) ◽  
pp. 383-386
Author(s):  
Patrick W. Darko
Keyword(s):  
Carleman Estimates ◽  
Stein Manifolds ◽  
Cauchy Riemann

Cohomology with bounds are used to globalize a result of Hörmander obtaining Carleman estimates for the Cauchy-Riemann operator on Stein manifolds.

scholarly journals Bott-Chern harmonic forms on Stein manifolds

2018 ◽  
Vol 147 (4) ◽  
pp. 1551-1564 ◽  
Author(s):  
Riccardo Piovani ◽  
Adriano Tomassini
Keyword(s):  
Harmonic Forms ◽  
Stein Manifolds
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