講演者 赤坂奎茉,前川拓海,箕輪悠希,柳田幸輝,Ye Liu
スケジュール
12月20日(土)
14:00 -- 14:30 赤坂奎茉(千葉大学)
(Op)lax Twisted Arrow (∞,n)-categories and its Applications to Condensations
14:50 -- 15:50 箕輪悠希(京都大学)
On the topological complexity of spaces with nontrivial fundamental groups
16:10 -- 17:10 Ye Liu(Xi'an Jiaotong-Liverpool University)
Holonomy Lie algebra of a geometric lattice
12月21日(日)
9:30 -- 10:30 前川拓海(東京大学)
Seiberg-Witten stable homotopy invariants via (∞,2)-functorial six-operations
10:45 -- 11:45 柳田幸輝(佐賀大学)
Dijkgraaf-Witten invariant in topological K-theory
アブストラクト
赤坂奎茉(千葉大学)
The Twisted Arrow (∞,n)-category and the Cospan (∞,n)-category
For an (∞-)category C, one can construct its twisted arrow category TwAr(C). For a 2-category, one may further relax commutativity by allowing (op)lax squares, Combining these two ideas, we are led to the notion of (op)lax twisted arrow (2-)categories TwAr(C)^{(op)lax}. In this work, we define (op)lax twisted arrow constructions for general (∞,n)-categories.
As an application, we show that these constructions allow one to reconstruct condensations, which in turn provide a convenient framework for describing idempotent completions of (∞,n)-categories.
前川拓海(東京大学)
Seiberg-Witten stable homotopy invariants via (∞,2)-functorial six-operations
Based on the works of Verdier and Grothendieck, and later developed by Kashiwara-Schapira, the six-functor formalism for sheaves enables us to understand cohomological duality theorems and transfer maps in terms of certain (stable) oo-categorical adjunction. After Gaitsgory-Rozenblyum, these six-operations fit into a single (oo,2)-functor out of the 2-category of correspondences. In this talk, we will present these modern points of view on the six-functor formalism, and as an application, we will see that the stable homotopy theoretic refinement of the Seiberg-Witten invariant defined for closed spin c four-manifold, introduced by Furuta and Bauer, does correspond to a 2-morphism in that (oo,2)-functoriality.
箕輪悠希(京都大学)
On the topological complexity of spaces with nontrivial fundamental groups
アブストラクト
柳田幸輝(佐賀大学)
Dijkgraaf-Witten invariant in topological K-theory
The Dijkgraaf–Witten (DW) invariant is a topological invariant of oriented closed 3-manifolds, defined by using the ordinary homology of the classifying space of a finite group. As its K-homological analogue, we consider KDW invariants. In this talk, I will explain a representation-theoretic method to compute KDW invariants and present explicit computations for several Brieskorn homology spheres with PSL_2 (F_p). These are the first explicit computations of DW invariants in cases where both the finite group and the fundamental group of the manifolds are non-nilpotent.
Ye Liu(Xi'an Jiaotong-Liverpool University)
Holonomy Lie algebra of a geometric lattice
Motivated by T. Kohno’s result on the holonomy Lie algebra of a hyperplane arrangement, we define the holonomy Lie algebra of a finite geometric lattice in a combinatorial way. For a solvable pair of lattices, we show that the holonomy Lie algebra is an almost-direct product of the holonomy Lie algebra of the sublattice and a free Lie subalgebra. This yields the structure of the holonomy Lie algebra of a finite hypersolvable (including supersolvable) lattice. As applications, we obtain the structure of the holonomy Lie algebra of (the Salvetti complex of) a supersolvable oriented matroid, and that of a hypersolvable arrangement.
世話人 浅尾泰彦(福岡大学) 石黒賢士(福岡大学) 岸本大祐(九州大学) 蔦谷充伸(九州大学) 宮内敏行(福岡大学)
資金 基盤研究 (C) 「J-準同型による球面の非安定ホモトピー群の大域構造の研究」(研究代表者:宮内敏行,研究課題番号:22K03326)