In topology, a branch of mathematics, a nilpotent space, first defined by Emmanuel Dror (1969), is a based topological space X such that * the fundamental group is a nilpotent group; * acts nilpotently on the higher homotopy groups , i.e., there is a central series such that the induced action of on the quotient group is trivial for all . Simply connected spaces and simple spaces are (trivial) examples of nilpotent spaces; other examples are connected loop spaces. The homotopy fiber of any map between nilpotent spaces is a disjoint union of nilpotent spaces. Moreover, the null component of the pointed mapping space , where K is a pointed, finite-dimensional CW complex and X is any pointed space, is a nilpotent space. The odd-dimensional real projective spaces are nilpotent spaces, while the projective plane is not. A basic theorem about nilpotent spaces states that any map that induces an integral homology isomorphism between two nilpotent space is a weak homotopy equivalence. For simply connected spaces, this theorem recovers a well-known corollary to the Whitehead and Hurewicz theorems. Nilpotent spaces are of great interest in rational homotopy theory, because most constructions applicable to simply connected spaces can be extended to nilpotent spaces. The Bousfield–Kan nilpotent completion of a space associates with any connected pointed space X a universal space through which any map of X to a nilpotent space N factors uniquely up to a contractible space of choices. Often, however, itself is not nilpotent but only an inverse limit of a tower of nilpotent spaces. This tower, as a pro-space, always models the homology type of the given pointed space X. Nilpotent spaces admit a good arithmetic localization theory in the sense of Bousfield and Kan cited above, and the unstable Adams spectral sequence strongly converges for any such space. Let X be a nilpotent space and let h be a reduced generalized homology theory, such as K-theory. If h(X)=0, then h vanishes on any Postnikov section of X. This follows from a theorem that states thatany such section is X-cellular. (Wikipedia).
NASA's newest X-ray telescope will have a lengthy structure that unfolds in space, allowing it to see high-energy objects like feeding black holes.
From playlist NuSTAR
Covariant Phase Space with Boundaries - Daniel Harlow
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From playlist Natural Sciences
What exactly is space? Brian Greene explains what the "stuff" around us is. Subscribe to our YouTube Channel for all the latest from World Science U. Visit our Website: http://www.worldscienceu.com/ Like us on Facebook: https://www.facebook.com/worldscienceu Follow us on Twitter: https:
From playlist Science Unplugged: Physics
Does space mean emptiness? How do you describe it?
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From playlist Science Unplugged: Physics
If you're not sure what a black hole is, or even if you just need a quick refresher, Brian Greene explains what lies behind these cosmological powerhouses. Subscribe to our YouTube Channel for all the latest from World Science U. Visit our Website: http://www.worldscienceu.com/ Like us o
From playlist Science Unplugged: Black Holes
This lecture is part of an online graduate course on Lie groups. We state Engel's theorem about nilpotent Lie algebras and sketch a proof of it. We give an example of a nilpotent Lie group that is not a matrix group. For the other lectures in the course see https://www.youtube.com/play
From playlist Lie groups
You're there, and I'm here. And we're all on the Earth. But where is the Earth? In the Solar System, obviously, which is in the Milky Way, and so on. Think about your place in the cosmos, your exact spot in the Universe relative to everything else. It's time to get your bearings, and once
From playlist Planets and Moons
Black Hole Apocalypse — Official Trailer
Join astrophysicist Janna Levin and others as they hunt for clues about the nature of black holes. NOVA’s “Black Hole Apocalypse” premieres January 10 on PBS. NOVA on Facebook: https://www.facebook.com/NOVAonline NOVA on Twitter: @novapbs NOVA on Instagram: @novapbs
From playlist Previews
Ask the Space Lab Expert: What is Space?
Have you ever wanted to go to Space? In this first episode of Space Lab, Brad and Liam from "World of the Orange" take you on an adventure to discover exactly what is Space. You'll find out about the solar system, the big bang, Sci-Fi movies that are becoming reality, and more!
From playlist What is Space? YouTube Space Lab with Liam and Brad
James Borger: The geometric approach to cohomology Part I
SMRI Seminar Course: 'The geometric approach to cohomology' Part I James Borger (Australian National University) Abstract: The aim of these two talks is to give an overview of the geometric aka stacky approach to various cohomology theories for schemes: de Rham, Hodge, crystalline and pr
From playlist SMRI Course: The geometric approach to cohomology
Is there any place in the Universe where there's truly nothing? Consider the gaps between stars and galaxies? Or the gaps between atoms? What are the properties of nothing?
From playlist Guide to Space
Ville Salo: Nilpotent endomorphisms of expansive group actions
We say a pointed dynamical system is asymptotically nilpotent if every point tends to zero. We study group actions whose endomorphism actions are nilrigid, meaning that for all asymptotically nilpotent endomorphisms the convergence to zero is uniform. We show that this happens for a large
From playlist Dynamical Systems and Ordinary Differential Equations
Higgs bundles and higher Teichmüller components (Lecture 2) by Oscar García-Prada
DISCUSSION MEETING : MODULI OF BUNDLES AND RELATED STRUCTURES ORGANIZERS : Rukmini Dey and Pranav Pandit DATE : 10 February 2020 to 14 February 2020 VENUE : Ramanujan Lecture Hall, ICTS, Bangalore Background: At its core, much of mathematics is concerned with the problem of classif
From playlist Moduli Of Bundles And Related Structures 2020
On characterization of monomial irreducible representations by Pooja Singla
DATE & TIME 05 November 2016 to 14 November 2016 VENUE Ramanujan Lecture Hall, ICTS Bangalore Computational techniques are of great help in dealing with substantial, otherwise intractable examples, possibly leading to further structural insights and the detection of patterns in many abstra
From playlist Group Theory and Computational Methods
Categorical non-properness in wrapped Floer theory - Sheel Ganatra
Joint IAS/Princeton/Montreal/Paris/Tel-Aviv Symplectic Geometry Topic: Categorical non-properness in wrapped Floer theory Speaker: Sheel Ganatra Affiliation: University of Southern California Date: April 02, 2021 For more video please visit http://video.ias.edu
From playlist Mathematics
Geometric deformations of orthogonal and symplectic Galois representations - Jeremy Booher
Jeremy Booher Stanford University November 19, 2015 https://www.math.ias.edu/seminars/abstract?event=87395 For a representation of the absolute Galois group of the rationals over a finite field of characteristic p, we would like to know if there exists a lift to characteristic zero with
From playlist Joint IAS/PU Number Theory Seminar
Commutative algebra 31 (Nullstellensatz)
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From playlist Commutative algebra
Modular Perverse Sheaves on the affine Flag Variety - Laura Rider
Virtual Workshop on Recent Developments in Geometric Representation Theory Topic: Modular Perverse Sheaves on the affine Flag Variety Speaker: Laura Rider Affiliation: University of Georgia Date: November 16, 2020 For more video please visit http://video.ias.edu
From playlist Virtual Workshop on Recent Developments in Geometric Representation Theory
Is the nothing of a black hole the same as empty space?
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From playlist Science Unplugged: Black Holes
Kevin Buzzard: Pre-adic and adic spaces
Find this video and other talks given by worldwide mathematicians on CIRM's Audiovisual Mathematics Library: http://library.cirm-math.fr. And discover all its functionalities: - Chapter markers and keywords to watch the parts of your choice in the video - Videos enriched with abstracts, b
From playlist Number Theory