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Poisson-Voronoi tessellations and fixed price in higher rank
By Amanda Wilkens
![Stable homology of braid groups with symplectic coefficients](/media/cache/video_light/uploads/video/2024-05-07_Petersen.mp4-02e4b37b08b4d31a5bc8706d66c76471-video-339dfc29f5d7136e6a7bcf8ea9ae0a67.jpg)
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Stable homology of braid groups with symplectic coefficients
By Dan Petersen
Appears in collection : 1923-2023, Centenaire de René Thom
The celebrated Lojasiewicz gradient inequality (L) has an important consequence; the length of a gradient trajectory, between two levels, is uniformly bounded. So, a trajectory has a limit when approaching a critical level. It has inspired Ren ́e Thom to formulate the conjecture that the trajectory has a tangent at the limit. I will describe various versions and extensions of inequality (L). I will state a variant of this inequality, which is valid for a map with values in a finite-dimensional vector space. It yields the boundedness of the volume of a submanifold transverse to the kernels of differentials of the map. This is an analogue of the boundedness of the length of gradient trajectories.