Výsledky vyhledávání - "Arf invariant"

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Topological field theory on r-spin surfaces and the Arf invariant

We give a combinatorial model for r-spin surfaces with parametrised boundary based on Novak (2015). The r-spin structure is encoded in terms of $\mathbb{Z}_r$-valued indices assigned to the edges of a polygonal decomposition. This combinatorial model

Externí odkaz: http://arxiv.org/abs/1802.09978

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Clifford algebras as twisted group algebras and the Arf invariant

Autor: Elduque, Alberto, Rodrigo-Escudero, Adrián

Publikováno v: Advances in Applied Clifford Algebras 28 (2018), no. 2, Art. 41, 15 pp

Some connections between quadratic forms over the field of two elements, Clifford algebras of quadratic forms over the real numbers, real graded division algebras, and twisted group algebras will be highlighted. This allows to revisit real Clifford a

Externí odkaz: http://arxiv.org/abs/1801.07002

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Simple Whitney towers, half-gropes and the Arf invariant of a knot

Autor: Schneiderman, Rob

Publikováno v: "Simple Whitney towers, half-gropes and the Arf invariant of a knot", Pacific Journal of Mathematics, Vol. 222, No. 1, Nov (2005)

A geometric characterization of the Arf invariant of a knot in the 3-sphere is given in terms of two kinds of 4-dimensional bordisms, half-gropes and Whitney towers. These types of bordisms have associated complexities class and order which filter th

Externí odkaz: http://arxiv.org/abs/math/0310304

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On the optimality of the Arf invariant formula for graph polynomials

Autor: Loebl, Martin, Masbaum, Gregor

We prove optimality of the Arf invariant formula for the generating function of even subgraphs, or, equivalently, the Ising partition function, of a graph.
Comment: Advances in Mathematics, 2010

Externí odkaz: http://arxiv.org/abs/0908.2925

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Local surgery formulas for quantum invariants and the Arf invariant

Autor: Kirby, Robion, Melvin, Paul

Publikováno v: Geom. Topol. Monogr. 7 (2004) 213-233

A formula for the Arf invariant of a link is given in terms of the singularities of an immersed surface bounded by the link. This is applied to study the computational complexity of quantum invariants of 3--manifolds.
Comment: Published by Geome

Externí odkaz: http://arxiv.org/abs/math/0410358

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The intersection of spheres in a sphere and a new geometric meaning of the Arf invariant

Autor: Ogasa, Eiji

Let S^3_i be a 3-sphere embedded in the 5-sphere S^5 (i=1,2). Let S^3_1 and S^3_2 intersect transversely. Then the intersection C of S^3_1 and S^3_2 is a disjoint collection of circles. Thus we obtain a pair of 1-links, C in S^3_i (i=1,2), and a pair

Externí odkaz: http://arxiv.org/abs/math/0003089

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