cell decompositions
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2021 ◽  
Vol 379 ◽  
pp. 107544
Author(s):  
Giovanni Cerulli Irelli ◽  
Francesco Esposito ◽  
Hans Franzen ◽  
Markus Reineke


Author(s):  
Gal Binyamini ◽  
Nicolai Vorobjov

Abstract The o-minimal structure generated by the restricted Pfaffian functions, known as restricted sub-Pfaffian sets, admits a natural measure of complexity in terms of a format  ${{\mathcal{F}}}$, recording information like the number of variables and quantifiers involved in the definition of the set, and a degree  $D$, recording the degrees of the equations involved. Khovanskii and later Gabrielov and Vorobjov have established many effective estimates for the geometric complexity of sub-Pfaffian sets in terms of these parameters. It is often important in applications that these estimates are polynomial in $D$. Despite much research done in this area, it is still not known whether cell decomposition, the foundational operation of o-minimal geometry, preserves polynomial dependence on $D$. We slightly modify the usual notions of format and degree and prove that with these revised notions, this does in fact hold. As one consequence, we also obtain the first polynomial (in $D$) upper bounds for the sum of Betti numbers of sets defined using quantified formulas in the restricted sub-Pfaffian structure.





2019 ◽  
Vol 295 (3-4) ◽  
pp. 993-1038
Author(s):  
Dylan Rupel ◽  
Thorsten Weist


2018 ◽  
Vol 13 (1-2) ◽  
pp. 169-183
Author(s):  
Toufik Mansour ◽  
Matthias Schork


2016 ◽  
Vol 16 (1) ◽  
Author(s):  
Xu Shen

AbstractWe give a new proof of the Lefschetz trace formula for Lubin-Tate spaces. Our proof is based on the locally finite cell decompositions of these spaces and on Mieda’s version of the Lefschetz trace formula for certain open adic spaces. This proof is rather different from the proofs of Strauch and Mieda, and it might be generalized to other Rapoport-Zink spaces as soon as there exist suitable cell decompositions. For example, in another paper we have proved a Lefschetz trace formula for some unitary group Rapoport-Zink spaces by using similar ideas as here.



2014 ◽  
Vol 2015 (18) ◽  
pp. 8372-8410 ◽  
Author(s):  
Victor Mouquin
Keyword(s):  


2014 ◽  
Vol 23 (06) ◽  
pp. 1450034 ◽  
Author(s):  
Toru Ikeda

We consider symmetries of spatial graphs in compact 3-manifolds described by smooth finite group actions. This paper provides a method for constructing an infinite family of hyperbolic spatial graphs with given symmetry by connecting spatial graph versions of hyperbolic tangles in 3-cells of polyhedral cell decompositions induced from triangulations of the 3-manifolds. This method is applicable also to the case of ideal triangulations.



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