A topological theory of unoriented SL(4) foams

Abstract

Unoriented SL(3) foams are two-dimensional CW complexes with generic singularities embedded in 3- and 4-manifolds. They naturally come up in the Kronheimer-Mrowka SO(3) gauge theory for 3-orbifolds and, in the oriented case, in a categorification of the Kuperberg bracket quantum invariant. The present paper studies the more technically complicated case of SL(4) foams. Combinatorial evaluation of unoriented SL(4) foams is defined and state spaces for it are studied. In particular, over a suitably localized ground ring, the state space of any web is free of the rank given by the number of its 4-colorings.

arXiv comment26 pages, many figures, comments welcome

References in corpus (10)

• Khovanov-Rozansky Homology and Topological Strings
• Knot invariants and higher representation theory
• The universal sl3-link homology
• Category O and sl(k) link invariants
• Knot homology via derived categories of coherent sheaves II, sl(m) case
• Quantum (sl_n, \land V_n) link invariant and matrix factorizations
• Universal construction of topological theories in two dimensions
• Homological Knot Invariants from Mirror Symmetry
• A deformation of Robert-Wagner foam evaluation and link homology
• The combinatorial and gauge-theoretic foam evaluation functors are not the same