11 citations · 36 across the 13 of their papers we have counts for
13 papers
Ribbon dioperads and modular ribbon properads
Wai-Kit Yeung
We define and study the notions of ribbon dioperads and modular ribbon properads. We give a Lie algebra structure on the colimit total object and the limit total object of a ribbon…
A higher Hodge extension of the Feigin-Tsygan Theorem
Wai-Kit Yeung
We show that the extended noncommutative de Rham complex of a cofibrant resolution, when completed at a certain Hodge filtration, is (reduced) quasi-isomorphic to the periodic cycl…
Survey on homological flips and homological flops
Wai-Kit Yeung
We give a survey for the results in [Yeu20a, Yeu20b, Yeu20c], which attempts to relate the derived categories under general classes of flips and flops. We indicate how the approach…
Shifted symplectic and Poisson structures on global quotients
Wai-Kit Yeung
For a derived stack obtained as a quotient of a derived affine scheme by a reductive group, we show that shifted symplectic structures can be characterized by the Cartan-de Rham co…
Representation homology of simply connected spaces
Yuri Berest, Ajay C. Ramadoss, Wai-Kit Yeung
Let be an affine algebraic group defined over field of characteristic zero. We study the derived moduli space of G-local systems on a pointed connected CW complex X trivial…
Weight truncation for wall-crossings in birational cobordisms
Wai-Kit Yeung
We develop the technique of weight truncation in the context of wall-crossings in birational cobordisms, parallel to that in [HL15, BFK19]. More precisely, for each such wall-cross…
Grothendieck duality and Greenlees-May duality on graded rings
Wai-Kit Yeung
We formulate and prove Serre's equivalence for -graded rings. When restricted to the usual case of -graded rings, our version of Serre's equivalence also sh…
Homological flips and homological flops
Wai-Kit Yeung
We introduce a notion of homological flips and homological flops. The former includes the class of all flips between Gorenstein normal varieties; while the latter includes the clas…
Pre-Calabi-Yau structures and moduli of representations
Wai-Kit Yeung
We establish a system of formal noncommutative calculus for differential forms and polyvector fields, which forms the foundations for the study of pre-Calabi-Yau categories. Using…
Vanishing theorems for representation homology and the derived cotangent complex
Yuri Berest, Ajay C. Ramadoss, Wai-kit Yeung
Let be a reductive affine algebraic group defined over a field of characteristic zero. In this paper, we study the cotangent complex of the derived -representation schem…
Representation homology of topological spaces
Yuri Berest, Ajay C. Ramadoss, Wai-kit Yeung
In this paper, we introduce and study representation homology of topological spaces, which is a natural homological extension of representation varieties of fundamental groups. We…
Relative Calabi-Yau completions
Wai-Kit Yeung
We generalize Keller's construction \cite{Kel11} of deformed -Calabi-Yau completions to the relative context. This gives a construction that extends any given dg functor $F : A…
Perverse Sheaves and Knot Contact Homology
Yuri Berest, Alimjon Eshmatov, Wai-kit Yeung
In this paper, which is mostly a research announcement, we give a new algebraic construction of knot contact homology in the sense of L. Ng [Ng05a]. For a link in $ {\mathbb R}…