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$\infty$ -groupoids and homotopy types

M. M. Kapranov, V. A. Voevodsky (1991)

Cahiers de Topologie et Géométrie Différentielle Catégoriques

A combinatorial characterization of planar 2-complexes

Jonathan L. Gross, Ronald H. Rosen (1981)

Colloquium Mathematicae

A conjecture on the unstable Adams spectral sequences for SO and U

Kathryn Lesh (2002)

Fundamenta Mathematicae

We give a systematic account of a conjecture suggested by Mark Mahowald on the unstable Adams spectral sequences for the groups SO and U. The conjecture is related to a conjecture of Bousfield on a splitting of the E₂-term and to an algebraic spectral sequence constructed by Bousfield and Davis. We construct and realize topologically a chain complex which is conjectured to contain in its differential the structure of the unstable Adams spectral sequence for SO. A filtration of this chain complex...

A duality on simplicial complexes.

Barr, Michael (2002)

Georgian Mathematical Journal

A Duality Theorem for Complex Manifolds.

Daniele Struppa, Cristina Turrini (1984/1985)

Mathematische Zeitschrift

A formula for topology/deformations and its significance

Ruth Lawrence, Dennis Sullivan (2014)

Fundamenta Mathematicae

The formula is $\partial e = (a d_{e}) b + \sum_{i = 0}^{\infty} (B_{i}) / i! {(a d_{e})}^{i} (b - a)$ , with ∂a + 1/2 [a,a] = 0 and ∂b + 1/2 [b,b] = 0, where a, b and e in degrees -1, -1 and 0 are the free generators of a completed free graded Lie algebra L[a,b,e]. The coefficients are defined by $x / (e^{x} - 1) = \sum_{n = 0}^{\infty} B ₙ / n! x ⁿ$ . The theorem is that ∙ this formula for ∂ on generators extends to a derivation of square zero on L[a,b,e]; ∙ the formula for ∂e is unique satisfying the first property, once given the formulae for ∂a and ∂b, along with the condition that the “flow” generated by e moves a to b in unit...