7 papers
Milnor numbers, Spanning Trees, and the Alexander-Conway Polynomial
Gregor Masbaum, Arkady Vaintrob
We study relations between the Alexander-Conway polynomial and Milnor higher linking numbers of links from the point of view of finite-type (Vassiliev) invariants. We gi…
A New Matrix-Tree Theorem
Gregor Masbaum, Arkady Vaintrob
The classical Matrix-Tree Theorem allows one to list the spanning trees of a graph by monomials in the expansion of the determinant of a certain matrix. We prove that in the case o…
Stable Spin Maps, Gromov-Witten Invariants, and Quantum Cohomology
Tyler J. Jarvis, Takashi Kimura, Arkady Vaintrob
We introduce the stack of r-spin maps. These are stable maps into a variety V from n-pointed algebraic curves of genus g, with the additional data of an r-spin structure on the cur…
Algebraic construction of Witten's top Chern class
Alexander Polishchuk, Arkady Vaintrob
We give a construction of Witten's "top Chern class" on the compactified moduli space of curves with higher spin structures and show that it satisfies most of the axioms proposed i…
Gravitational Descendants and the Moduli Space of Higher Spin Curves
Tyler J. Jarvis, Takashi Kimura, Arkady Vaintrob
The purpose of this note is introduce a new axiom (called the Descent Axiom) in the theory of -spin cohomological field theories. This axiom explains the origin of gravitational…
Noncommutative Rational Functions and Farber's Invariants of Boundary Links
Vladimir Retakh, Christophe Reutenauer, Arkady Vaintrob
In [2] M. Farber constructed invariants of m-component boundary links with values in algebra of noncommutative rational functions. In this paper we simplify his constructions and e…