topology, universal coefficient theorems establish relationships between homology groups (or cohomology groups) with different coefficients. For instance...

mathematical theory of artificial neural networks, universal approximation theorems are theorems of the following form: Given a family of neural networks...

the homology group in this case is a vector space over Q. The universal coefficient theorem, in a very simple torsion-free case, shows that these definitions...

H} defined in algebraic topology (as a special case of the universal coefficient theorem). The conventional term Hodge cycle therefore is slightly inaccurate...

Eilenberg around 1950. It was first applied to the Künneth theorem and universal coefficient theorem in topology. For modules over any ring, Tor was defined...

Eilenberg and Saunders MacLane (1942), and applied to topology (the universal coefficient theorem for cohomology). For modules over any ring, Ext was defined...

Combining this proof with the universal coefficient theorem nearly yields the usual Lefschetz theorem for cohomology with coefficients in any field of characteristic...

approximation theorem (algebraic topology) Stallings–Zeeman theorem (algebraic topology) Sullivan conjecture (homotopy theory) Universal coefficient theorem (algebraic...

homology Relative homology Mayer–Vietoris sequence Excision theorem Universal coefficient theorem Cohomology List of cohomology theories Cocycle class Cup...

theorem Poincaré duality theorem Seifert–van Kampen theorem Universal coefficient theorem Whitehead theorem Algebraic K-theory Exact sequence Glossary of algebraic...

knowing each individual integral cohomology group, because of the universal coefficient theorem. However, the advantage of the cohomology groups is that there...

Since every Riemann surface has a universal cover which is a simply connected Riemann surface, the uniformization theorem leads to a classification of Riemann...

corresponding to coefficient homomorphism Hom ⁡ ( G , H ) {\displaystyle \operatorname {Hom} (G,H)} . This follows from the Universal coefficient theorem for cohomology...

Y)\to H^{i}(X)\to H^{i}(Y)\to H^{i+1}(X,Y)\to \cdots } The universal coefficient theorem describes cohomology in terms of homology, using Ext groups...

orientable or not. This follows from an application of the universal coefficient theorem. Let R {\displaystyle R} be a commutative ring. For R {\displaystyle...

. Alternatively, the result can also be obtained using the Universal coefficient theorem. Complex projective space Quaternionic projective space Lens...

ones-- which can be seen either by direct computation, the universal coefficient theorem or even Poincaré duality. If a torus is punctured and turned...

M {\displaystyle H_{i}M\simeq H^{n-i}M} , together with the universal coefficient theorem, which gives an identification f H n − i M ≡ H o m ( H n − i...

{\displaystyle H^{n}(X^{\text{an}},\mathbb {C} )} , which by the universal coefficient theorem is in its turn isomorphic to H n ( X an , Q ) ⊗ Q C . {\displaystyle...

S=0} at absolute zero, as required by Nernst's theorem. In practice the absolute Seebeck coefficient is difficult to measure directly, since the voltage...

{\displaystyle X} with compact supports and coefficients in Q {\displaystyle \mathbb {Q} } . The universal coefficient theorem for H 2 ( X ; Q ) {\displaystyle H^{2}(X;\mathbb...

output of the Universal Coefficient Theorem when applied to a cohomology theory such as Čech cohomology or (in the case of real coefficients) De Rham cohomology...

abelian group Ray–Singer torsion Torsion-free abelian group Universal coefficient theorem Roman 2008, p. 115, §4 Ernst Kunz, "Introduction to Commutative...

\mathbb {Z} ),\pi _{n}(Y))\cong 1} for the Ext functor. The Universal coefficient theorem then simplifies and claims: H n ( Y , π n ( Y ) ) ≅ Hom Z ⁡...

shows for instance higher homotopy groups are abelian. Universal coefficient theorem Dold–Thom theorem See also: Characteristic class, Postnikov tower, Whitehead...

Fourier expansion coefficients. The sampling theorem is usually formulated for functions of a single variable. Consequently, the theorem is directly applicable...

universal coefficient theorem provides a mechanism to calculate the homology with R coefficients in terms of homology with usual integer coefficients...

that the homology groups are always torsion-free using the universal coefficient theorem. This implies that the middle homology group is determined by...

is so-called strong mixing coefficient. A simplified formulation of the central limit theorem under strong mixing is: Theorem—Suppose that { X 1 , … , X...

Richard E. Stearns improved the efficiency of the universal Turing machine. Consequent to the theorem, for every deterministic time-bounded complexity...