scholarly journals On the GIT quotient space of quintic surfaces

2018 ◽  
Vol 371 (6) ◽  
pp. 4251-4276 ◽  
Author(s):  
Patricio Gallardo
Keyword(s):  
Quotient Space ◽  
Git Quotient

scholarly journals On nonacyclicity of the quotient space of R3 by the solenoid

2003 ◽  
Vol 133 (1) ◽  
pp. 65-68 ◽  
Author(s):  
Umed H. Karimov ◽  
Dušan Repovš
Keyword(s):  
Quotient Space

scholarly journals Perverse Schobers and Wall Crossing

2017 ◽  
Vol 2019 (18) ◽  
pp. 5777-5810 ◽  
Author(s):  
W Donovan
Keyword(s):  
Invariant Theory ◽  
Local System ◽  
Vector Spaces ◽  
Geometric Invariant ◽  
Perverse Sheaf ◽  
Derived Equivalences ◽  
Grothendieck Groups ◽  
Wall Crossing ◽  
Git Quotient ◽  
Cohomology Complex

Abstract For a balanced wall crossing in geometric invariant theory (GIT), there exist derived equivalences between the corresponding GIT quotients if certain numerical conditions are satisfied. Given such a wall crossing, I construct a perverse sheaf of categories on a disk, singular at a point, with half-monodromies recovering these equivalences, and with behaviour at the singular point controlled by a GIT quotient stack associated to the wall. Taking complexified Grothendieck groups gives a perverse sheaf of vector spaces: I characterize when this is an intersection cohomology complex of a local system on the punctured disk.

scholarly journals Alternative Approach to Infinity

1974 ◽  
Vol 64 ◽  
pp. 99-99
Author(s):  
Peter G. Bergmann
Keyword(s):  
Large Class ◽  
Riemannian Manifolds ◽  
Quotient Space ◽  
Three Dimensional ◽  
Cauchy Data ◽  
Space Time ◽  
Equivalence Classes ◽  
Null Infinity ◽  
Alternative Approach ◽  
Dimensional Domain

Following Penrose's construction of space-time infinity by means of a conformal construction, in which null-infinity is a three-dimensional domain, whereas time- and space-infinities are points, Geroch has recently endowed space-infinity with a somewhat richer structure. An approach that might work with a large class of pseudo-Riemannian manifolds is to induce a topology on the set of all geodesics (whether complete or incomplete) by subjecting their Cauchy data to (small) displacements in space-time and Lorentz rotations, and to group the geodesics all of whose neighborhoods intersect into equivalence classes. The quotient space of geodesics over equivalence classes is to represent infinity. In the case of Minkowski, null-infinity has the usual structure, but I0, I+, and I- each become three-dimensional as well.

Quotients of Essentially Euclidean Spaces

2019 ◽  
Vol 62 (1) ◽  
pp. 71-74
Author(s):  
Tadeusz Figiel ◽  
William Johnson
Keyword(s):  
Normed Space ◽  
Quotient Space ◽  
Euclidean Spaces ◽  
Quantitative Version ◽  
Finite Dimensional ◽  
Dimensional Normed Space

AbstractA precise quantitative version of the following qualitative statement is proved: If a finite-dimensional normed space contains approximately Euclidean subspaces of all proportional dimensions, then every proportional dimensional quotient space has the same property.

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