Showing posts with label geometry/topology. Show all posts
Showing posts with label geometry/topology. Show all posts

#OpusSolve

Hodge conjecture

Let X be a non-singular complex projective manifold. Then every Hodge class on X is a linear combination with rational coefficients of the cohomology classes of complex subvarieties of X.

Story

Errata

Presented here are wrong/incorrect approaches to tackling the problem. These are offered as case studies of what to avoid.

+Poincarรฉ conjecture

+Hodge conjecture

Let X be a non-singular complex projective manifold. Then every Hodge class on X is a linear combination with rational coefficients of the cohomology classes of complex subvarieties of X.

+noncommutative geometry

+topology

+geometry

+geometry and topology

+brane

A brane (short for membrane) is some mathematical generalization of a category to one (1) or more higher dimensions.

My portfolio is a twenty-six dimensional (26-dim) toy [๐Ÿงฉpuzzleware] with braneworld structure according to pitch class:
0-brane = particle
1-brane = string
2-brane = manifold/sheet/tape
3-brane = cell
.
.
.
25-brane
(see also Egglepple, mesh, patch, walk)

+supergeometry

+coverage

A coverage is the twistorspace posture (ie. formation) for surjectively graphing a [supersymmetric] zone on(to) some pitch.

As cryptographic shape schemes [puzzles๐Ÿงฉ], coverages are fundamentally mutable and dynamic; spanning the entire range of branes(SMALL + BIG). A coverage can be (strategically) both preventive and responsive. (see also #coverage, egg, epp, patchwork, cassette, Honne Bay)

+loop

Mathematically, a loop is a closed๐Ÿ”’ string with no knots or tanglements whose path starts and terminates at the same point. Ludologically, a loop is a simple infinite walk; such that it encloses leaves (reading frames) on a loopstring. In both cases, a loop is continuous with either no nuts, or has homologically conjoined endpoints.
/// For sake of stew choreography, a loop is just a completed walk that has become unavailable for recycling.

+twistorspace

Ludologically, twistorspace or "slot" is a complex configuration space (eg. geotop) of solutions to the twistor identity ||f(u,u)=0||. Because a fibor is encoded to close๐Ÿ”’ its loopstring the exact same way every time (ascertained from the uniqueness property), there must exist an acoustic bound in place enforcing these conformations (bubble or vacuum); without such a (force) field, the fibor (as measured in ¢ents) would not bifurcate (into MONEY or bubblegum) as a function of symmetry-breaking.
/// +We assume that each twistor field is unique to some fibor. Essentially, this is a mapped spinor. The 'spin' (an object's spinning metric signature) here is identifiable with the quantum fields of arbitrary spin.

+Everything in twistorspace is dyadic (u,u).
Twistorspace' complexity is curvilinear (T)*.More accurately, sesquilinear. (see also handicap, jukespace, coverage)

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