transversality theorem
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Author(s):  
Michael McQuillan

AbstractWe prove a best possible transversality theorem for maps from manifolds to orbifolds, and, more generally arbitrary differentiable Deligne–Mumford classifying champs, 0.1, of groupoids $$R\rightrightarrows U$$ R ⇉ U in separated, 0.2, manifolds. En passant, the essentially finite dimensional linear algebra nature of jet transversality is isolated.



2021 ◽  
Vol S (1) ◽  
pp. 537-541
Author(s):  
G. V. Shunmugapriya ◽  
M. Davamani Christober




Axioms ◽  
2020 ◽  
Vol 9 (2) ◽  
pp. 37 ◽  
Author(s):  
Donal O’Regan

This paper considers the topological transversality theorem for general multivalued maps which have selections in a given class of maps.



Mathematics ◽  
2020 ◽  
Vol 8 (3) ◽  
pp. 427
Author(s):  
Donal O’Regan

A new simple result is presented which immediately yields the topological transversality theorem for coincidences.



Mathematics ◽  
2020 ◽  
Vol 8 (3) ◽  
pp. 304
Author(s):  
Donal O’Regan

A simple theorem is presented that automatically generates the topological transversality theorem and Leray–Schauder alternatives for weakly upper semicontinuous, weakly compact maps. An application is given to illustrate our results.



Mathematics ◽  
2019 ◽  
Vol 7 (11) ◽  
pp. 1113 ◽  
Author(s):  
Donal O’Regan

This paper considers a topological transversality theorem for multivalued maps with continuous, compact selections. Basically, this says, if we have two maps F and G with continuous compact selections and F ≅ G , then one map being essential guarantees the essentiality of the other map.



Mathematics ◽  
2019 ◽  
Vol 7 (8) ◽  
pp. 682
Author(s):  
Donal O’Regan

We present general Leray-Schauder type theorems for compact acyclic Multifunctions, using the topological transversality theorem by the author.



2019 ◽  
Vol 168 (3) ◽  
pp. 519-533
Author(s):  
NHAN NGUYEN ◽  
SAURABH TRIVEDI

AbstractWe present a definable smooth version of the Thom transversality theorem. We show further that the set of non-transverse definable smooth maps is nowhere dense in the definable smooth topology. Finally, we prove a definable version of a theorem of Trotman which says that the Whitney (a)-regularity of a stratification is necessary and sufficient for the stability of transversality.



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