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Longer titles found: Persistent Betti number (view)

searching for Betti number 14 found (96 total)

L² cohomology (541 words) [view diff] no match in snippet view article find links to article

In mathematics, L2 cohomology is a cohomology theory for smooth non-compact manifolds M with Riemannian metric. It is defined in the same way as de Rham

Homogeneous coordinate ring (1,245 words) [view diff] no match in snippet view article find links to article

In algebraic geometry, the homogeneous coordinate ring R of an algebraic variety V given as a subvariety of projective space of a given dimension N is

Invariant factor (259 words) [view diff] exact match in snippet view article find links to article

The nonnegative integer r {\displaystyle r} is called the free rank or Betti number of the module M {\displaystyle M} , while a 1 , … , a m {\displaystyle

Supersingular variety (318 words) [view diff] exact match in snippet view article find links to article

supersingular if the rank of its Néron–Severi group is equal to its second Betti number. A surface is called Artin supersingular if its formal Brauer group has

Elementary divisors (442 words) [view diff] exact match in snippet view article find links to article

The nonnegative integer r {\displaystyle r} is called the free rank or Betti number of the module M {\displaystyle M} . The module is determined up to isomorphism

Clifford's theorem on special divisors (734 words) [view diff] exact match in snippet view article find links to article

its canonical embedding, as the largest index i for which the graded Betti number βi, i + 2 is zero. Green and Robert Lazarsfeld showed that a(C) + 1 is

Arithmetic hyperbolic 3-manifold (1,714 words) [view diff] exact match in snippet view article find links to article

positive first Betti number). Arithmetic manifolds can be used to give examples of manifolds with large injectivity radius whose first Betti number vanishes

Novikov ring (740 words) [view diff] exact match in snippet view article find links to article

and its torsion part. The rank of the free part is called the Novikov Betti number and is denoted by b p ( ξ ) {\displaystyle b_{p}(\xi )} . The number

Systolic geometry (3,932 words) [view diff] exact match in snippet view article find links to article

there exists an 8-manifold with exceptional Spin(7) holonomy and 4-th Betti number 1, then the value 14 is in fact optimal. Manifolds with Spin(7) holonomy

David Mumford (2,067 words) [view diff] exact match in snippet view article find links to article

characteristic p where the geometric genus is non-zero, but the second Betti number is equal to the rank of the Néron–Severi group. Further such examples

Prakash Belkale (606 words) [view diff] exact match in snippet view article find links to article

a certain homogeneous polynomial whose degree is equal to the first betti number of G. These polynomials appear in the study of electrical circuits and

Co-Hopfian group (1,533 words) [view diff] exact match in snippet view article find links to article

Euler characteristic (or with nonzero simplicial volume or nonzero L2-Betti number), then G is co-Hopfian. If G is the fundamental group of a closed connected

Exotic sphere (3,802 words) [view diff] exact match in snippet view article find links to article

that it is not the boundary of any smooth 8-manifold with vanishing 4th Betti number, and has no orientation-reversing diffeomorphism to itself; either of

Glossary of algebraic topology (7,555 words) [view diff] exact match in snippet view article find links to article

based space A pair (X, x0) consisting of a space X and a point x0 in X. Betti number Bing–Borsuk conjecture See Bing–Borsuk conjecture. Bockstein homomorphism