Questions tagged [reference-request]
This tag is for questions seeking external references (books, articles, etc.) about a particular subject. Please do not use this as the only tag for a question.
22,195 questions
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Regularity of Boundary Layer for Navier Stokes Equation On a Riemannian Manifold With Boundary
The concept of a boundary layer in fluid dynamics is a ubiquitous in engineering applications involving the Navier Stokes Equation.
For a simple example: Consider flow past a semi-infinite flat plate (...
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Can the isomorphism of fundamental groups be restated as one of homology with local coefficients?
Here is an exercise from Allen Hatcher's Algebraic Topology after section 4.2:
Show that a map $f :X→Y$ of connected CW complexes is a homotopy equivalence
if it induces an isomorphism on $π_1$ and ...
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References: Precedence for studying symmetries of systems of foliations (hopefully in an analytic geometry sense)?
I'm curious if there is literature surrounding symmetries of foliations or subsets therein with sufficient decay behavior, especially with cone "end" behavior, using "cut and paste"...
- 1,258
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A variety admitting a cohomological decomposition of the diagonal but not a Chow-theoretic version
Let $X$ be a smooth projective complex variety. If $X$ admits a Chow decomposition of the diagonal then it admits a cohomological decomposition of the diagonal. Indeed one can take the cohomological ...
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Reference to a proof of a theorem on integrability of Lie algebra cocycles
I recently cam across this theorem in a set of lecture notes (without proof) and I am currently looking for a reference where I can find the proof.
If $U\colon G\to V$ is a $1$-cocycle of $G$ with ...
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Looking for Sources that Reconcile Differential Geometry with Calculus of Variations
My question might be eyewash. If not, then I am unsurprised if this topic is low-hanging in the world of analysis and geometry; I've yet to see it with my greenhorn eyes.
My reading background:
I've ...
- 1,881
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Prerequisites and targetted audiences for Polya & Szego Problems and Theorems in Analysis
I'm studying mathematical analysis the most from the two volume set Vladimir Zorich Mathematical Analysis. I've almost done the first volume. With ample grit and internet researching skills, I ...
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Reference request for $\dim_K(P^m(u))=m\deg(P)$
Let $K$ be an arbitrary field, and let $u$ be an endomorphism of a finite dimension $K$-vector space $V$.
Let $\chi_u=P_1^{m_1}\cdots P_r^{m_r}$ be the factorization of the characteristic polynomial ...
- 17k
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Reference for classical action of the standard height function on the two-torus written as sum of elementary and elliptic integrals?
The height function of the two torus $\mathbb{T}^2$ is a standard example. It has $2$ hyperbolic points and $2$ elliptic points. I was wondering if there exists a reference that computes the classical ...
- 5,079
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Proof on the Li -Yau Inequality
The standard Li Yau Estimate with a curvature term states that:
Let $(M^n,g)$ be a complete Riemannian manifold with $\text{Ric}\ge -(n-1)Hg, \space H\ge0$ , and let $u(x,t)>0$ solve the heat ...
- 1,973
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The name of an algebraic structure satisfying $y*(y*x)=x=(x*y)*y$
This is an abstract algebra exercise. See also here.
Let $(X,*)$ be an algebraic structure with $*$ a binary operation. If
$$ (x*y)*y=x=y*(y*x),\qquad \forall x,y\in X$$
show that $*$ is commutative.
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Reference Request: Non-trivial finite group can't act freely on contractible manifold
In the answers to this question here it was stated that:
"A nontrivial finite group cannot act freely on a contractible manifold."
This seems to be a straightforward result from group ...
- 3,657
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Books that cover multilinear algebra [duplicate]
We are currently following a course on multilinear algebra: tensor product and tensor - symmetric - exterior algebras.
The textbook for our course mainly deals with "mono"-linear algebra, ...
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Exercise I.3.19 in Hartshorne — still an open problem?
For completion, I here state what Exercise I.3.19 in Hartshorne's Algebraic Geometry (1977) says
3.19. Automorphisms of $\mathbb{A}^n$. Let $\varphi:\mathbb{A}^n \to \mathbb{A}^n$ be a morphism of $\...
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Fekete's lemma for Banach lattice sequences
Recall that a real sequence $(a_n)$ is sub-additive if
$$\forall n, m \in\mathbb{N}^*, ~ a_{n + m} \leq a_n + a_m$$
Fekete's lemma states that if $(a_n)_{n\in\mathbb{N}^*} \in \mathbb{R}^{\mathbb{N}^*}...
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