4 citations · 12 across the 11 of their papers we have counts for
11 papers
Embedding calculus and Vassiliev spectral sequence
Syunji Moriya
Vassiliev spectral sequence and Sinha spectral sequence are both related to cohomology of the space of long knots . Although they have different origins…
A note on non-simply connected rational homotopy models
Syunji Moriya
In their generalization of the rational homotopy theory to non-simply connected spaces, Gómez-Tato--Halperin--Tanré adopted local systems of commutative differential graded algebra…
Sinha's spectral sequence for long knots in codimension one and non-formality of the little 2-disks operad
Syunji Moriya
We compute some differentials of Sinha's spectral sequence for cohomology of the space of long knots modulo immersions in codimension one, mainly over a field of characteristic …
Models for knot spaces and Atiyah duality
Syunji Moriya
Let be the space of smooth embeddings from the circle to a closed manifold of dimension . We study a cosimplicial model of i…
On Cohen-Jones isomorphism in string topology
Syunji Moriya
The loop product is an operation in string topology. Cohen and Jones gave a homotopy theoretic realization of the loop product as a classical ring spectrum for a manifol…
The space of short ropes and the classifying space of the space of long knots
Syunji Moriya, Keiichi Sakai
We prove affirmatively the conjecture raised by J. Mostovoy; the space of short ropes is weakly homotopy equivalent to the classifying space of the topological monoid (or category)…
Non-formality of the odd dimensional framed little balls operads
Syunji Moriya
We prove that the chain operad of the framed little balls (or disks) operad is not formal as a non-symmetric operad over the rationals if the dimension of their balls is odd and gr…
Multiplicative formality of operads and Sinha's spectral sequence for long knots
Syunji Moriya
Lambrechts, Turchin and Volić proved the Bousfield-Kan type rational homology spectral sequence associated to the -th Kontsevich operad collapses at -page if . The…
Steenrod operations on bar complex
Syunji Moriya
We define a chain map of the form $\E(k)\otimes BA^{\otimes k}\longrightarrow BA$, where $\E$ is a combinatorial -operad called the sequence operad, and is the bar c…
The de Rham homotopy theory and differential graded category
Syunji Moriya
This paper is a generalization of arXiv:0810.0808. We develop the de Rham homotopy theory of not necessarily nilpotent spaces, using closed dg-categories and equivariant dg-algebra…
Rational homotopy theory and differential graded category
Syunji Moriya
We propose a generalization of Sullivan's de Rham homotopy theory to non-simply connected spaces. The formulation is such that the real homotopy type of a manifold should be the cl…