1,363 research outputs found
A categorification of the Jones polynomial
We construct a bigraded cohomology theory of links whose Euler characteristic
is the Jones polynomial.Comment: latex, 51 pages, 72 eps figures, to appear in Duke Mathematical
Journa
Computations in formal symplectic geometry and characteristic classes of moduli spaces
We make explicit computations in the formal symplectic geometry of Kontsevich
and determine the Euler characteristics of the three cases, namely commutative,
Lie and associative ones, up to certain weights.From these, we obtain some
non-triviality results in each case. In particular, we determine the integral
Euler characteristics of the outer automorphism groups Out F_n of free groups
for all n <= 10 and prove the existence of plenty of rational cohomology
classes of odd degrees. We also clarify the relationship of the commutative
graph homology with finite type invariants of homology 3-spheres as well as the
leaf cohomology classes for transversely symplectic foliations. Furthermore we
prove the existence of several new non-trivalent graph homology classes of odd
degrees. Based on these computations, we propose a few conjectures and problems
on the graph homology and the characteristic classes of the moduli spaces of
graphs as well as curves.Comment: 33 pages, final version, to appear in Quantum Topolog
A non-partitionable Cohen-Macaulay simplicial complex
A long-standing conjecture of Stanley states that every Cohen-Macaulay
simplicial complex is partitionable. We disprove the conjecture by constructing
an explicit counterexample. Due to a result of Herzog, Jahan and Yassemi, our
construction also disproves the conjecture that the Stanley depth of a monomial
ideal is always at least its depth.Comment: Final version. 13 pages, 2 figure
Pieri resolutions for classical groups
We generalize the constructions of Eisenbud, Fl{\o}ystad, and Weyman for
equivariant minimal free resolutions over the general linear group, and we
construct equivariant resolutions over the orthogonal and symplectic groups. We
also conjecture and provide some partial results for the existence of an
equivariant analogue of Boij-S\"oderberg decompositions for Betti tables, which
were proven to exist in the non-equivariant setting by Eisenbud and Schreyer.
Many examples are given.Comment: 40 pages, no figures; v2: corrections to sections 2.2, 3.1, 3.3, and
some typos; v3: important corrections to sections 2.2, 2.3 and Prop. 4.9
added, plus other minor corrections; v4: added assumptions to Theorem 3.6 and
updated its proof; v5: Older versions misrepresented Peter Olver's results.
See "New in this version" at the end of the introduction for more detail
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