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• Tangent bundles
  ...K$ is the set of $1$-chains over ring $R$ generated by the $1$-dimensional star of the vertex $A$: ...the edges adjacent to $A$, we can also think of all $1$-''chains'' in the star of $A$ as directions at $A$. They are subject to algebraic operations on ch
  16 KB (2,753 words) - 13:55, 16 March 2016
• Nerve of cover
  Given a simplicial complex $K$ and a vertex $A$ in $K$, the ''star'' of $A$ in $K$ is the collection of all simplices in $K$ that contain $A$: ...easy to prove that this is a subcomplex of $K$. We will also use the word "star" for the union of ${A}$ and the interiors of all the simplices that contain
  8 KB (1,389 words) - 13:35, 12 August 2015
• Combinatorial cell complexes
  ...tion. First, by the above theorem, $K$ has to be a graph. Furthermore, the star of a vertex with more than one adjacent edge isn't homeomorphic to the open Of course, we recognize this collection of simplices as the star of vertex $A$.
  34 KB (5,710 words) - 22:27, 18 February 2016
• Advanced Topology: exercises
  #A set $Y \subset {\bf R}^n$ is called star-shaped if there is $a\in Y$ such that for any $x \in Y$ the segment from $x #Define the Hodge $\star$ operator for discrete forms on the plane. Give examples.
  9 KB (1,487 words) - 18:18, 9 May 2013
• Homology groups of graphs
  ...ment of our group including zero (white). Meanwhile, we mark one -- with a star -- in each as a representative. ...ps of the graph of $n$ edges arranged in (a) a string, (b) a circle, (c) a star.
  28 KB (4,685 words) - 17:25, 28 November 2015
• Discrete forms
  ...of $K$ is the set of $1$-chains over $R$ generated by the $1$-dimensional star of the vertex $A$: ...the edges adjacent to $A$, we can also think of all $1$-''chains'' in the star of $A$ as directions at $A$. They are subject to algebraic operations on ch
  35 KB (6,055 words) - 13:23, 24 August 2015
• Advanced Topology -- Spring 2013 -- final exam
  #A set $Y \subset {\bf R}^n$ is called star-shaped if there is $a\in Y$ such that for any $x \in Y$ the segment from $x #A set $Y \subset {\bf R}^n$ is called star-shaped if there is $a\in Y$ such that for any $x \in Y$ the segment from $x
  3 KB (532 words) - 15:09, 8 May 2013
• Calculus on cubical complexes
  ...of $K$ is the set of $1$-chains over $R$ generated by the $1$-dimensional star of the vertex $A$: ...the edges adjacent to $A$, we can also think of all $1$-''chains'' in the star of $A$ as directions at $A$. They are subject to algebraic operations on ch
  36 KB (6,218 words) - 16:26, 30 November 2015
• Topology II -- Spring 2014
  ...e chapters below within a week. The most current material is marked with $\star$. #[[Homology theory]] $\star$
  3 KB (445 words) - 16:04, 20 May 2014
• Topology I -- Fall 2013
  ...e chapters below within a week. The most current material is marked with $\star$. $\star$
  7 KB (881 words) - 19:04, 10 December 2013
• Forms in Euclidean spaces
  ...ertex $A$ consists, as before, of the edges adjacent to $A$, i.e., the $1$-star $St(A)$. However, this time the algebra of $T_A(K)$ doesn't come from the $ supplies the star with algebra of edges.
  44 KB (7,778 words) - 23:32, 24 April 2015
• Hodge duality
  ...e $V$ of dimension $n$. For each integer $k$ with $0 ≤ k ≤ n$, the ''Hodge star operator'' establishes a one-to-one mapping from the space of $k$-vectors $ $$\star : \Lambda ^k (V)\rightarrow \Lambda ^{n-k}(V).$$
  613 bytes (95 words) - 18:10, 27 August 2015
• Computational science training: 2012
  ...e_and_Hodge_duality:_part_1#Hodge_duality_in_.24.7B.5Cbf_R.7D.5E2.24|Hodge star operator]].
  5 KB (732 words) - 17:42, 8 April 2013
• Integrals of functions of several variables
  The motion of two planets (or a star and a planet, or a planet and a satellite, etc.) is governed by a single fo
  73 KB (13,324 words) - 14:06, 24 November 2018
• Cubical tangent bundle
  ...int union of all ''tangent spaces'' with each simply the $1$-dimensional [[star]] of the vertex:
  3 KB (438 words) - 04:30, 27 May 2013
• Manifolds model a curved universe
  Experiment 1: with light from a star passing the sun and deviating from straight line.
  10 KB (1,588 words) - 17:11, 27 August 2015
• Current students' projects
  **the [[Hodge star operator]] for forms,
  4 KB (527 words) - 14:04, 25 August 2013
• Multilinear algebra
  ...of $K$ is the set of $1$-chains over $R$ generated by the $1$-dimensional star of the vertex $A$: [[image:boundary on star.png|center]]
  49 KB (8,852 words) - 00:30, 29 May 2015
• Discrete Calculus. An Introduction
  ##[[Discrete Hodge star operator]]
  4 KB (466 words) - 19:07, 8 July 2014
• Nerve of cover of sphere
  ...[[tetrahedron]], as a 2-dimensional [[simplicial complex]], and use the [[star of vertex|stars]] of its vertices to build an open cover on the sphere. Of
  763 bytes (118 words) - 12:22, 12 August 2015

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