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作者:Kai Cieliebak , Alexandru Oancea
来源:[J].Algebraic & Geometric Topology, 2018, Vol.18 (4), pp.1953-2130
摘要:We give a definition of symplectic homology for pairs of filled Liouville cobordisms, and show that it satisfies analogues of the Eilenberg–Steenrod axioms except for the dimension axiom. The resulting long exact sequence of a pair generalizes various earlier long exact sequ...
作者:Ruizhi Huang , Jie Wu
来源:[J].Algebraic & Geometric Topology, 2017, Vol.17 (4), pp.2125-2144
摘要:We prove a necessary condition for the existence of an A p –structure on mod p spaces, and also derive a simple proof for the finiteness of the number of mod p A p –spaces of given rank. As a direct applic...
作者:Ismaël Soudères
来源:[J].Algebraic & Geometric Topology, 2018, Vol.18 (2), pp.635-685
摘要:We prove the Beilinson–Soulé vanishing conjecture for motives attached to the moduli spaces ℳ 0 , n of curves of genus 0 with n marked points. As part of the proof, we also show that these motives are mixed Tate. As a consequence of Levine’s work, we thus obtain a well-...
作者:Prayat Poudel , Nikolai Saveliev
来源:[J].Algebraic & Geometric Topology, 2017, Vol.17 (5), pp.2635-2685
摘要:Singular instanton Floer homology was defined by Kronheimer and Mrowka in connection with their proof that Khovanov homology is an unknot detector. We study this theory for knots and two-component links using equivariant gauge theory on their double branched covers. We show that ...
作者:Kohei Tanaka
来源:[J].Algebraic & Geometric Topology, 2018, Vol.18 (2), pp.779-796
摘要:This paper presents a discrete analog of topological complexity for finite spaces using purely combinatorial terms. We demonstrate that this coincides with the genuine topological complexity of the original finite space. Furthermore, we study the relationship with simplicial comp...
作者:Yi Ni , Xingru Zhang
来源:[J].Algebraic & Geometric Topology, 2018, Vol.18 (1), pp.441-492
摘要:We show that on a hyperbolic knot K in S 3 , the distance between any two finite surgery slopes is at most 2 , and consequently, there are at most three nontrivial finite surgeries. Moreover, in the case where K admits three nontrivial finite surgeries, K must be the pretzel...
作者:Beatrice Bleile , Imre Bokor , Jonathan A Hillman
来源:[J].Algebraic & Geometric Topology, 2018, Vol.18 (7), pp.3749-3788
摘要:Turaev conjectured that the classification, realization and splitting results for Poincaré duality complexes of dimension 3 ( PD 3 –complexes ) generalize to PD n –complexes with ( n − 2 ) –connected universal cover for n ≥ 3 . Baues and Bleile showed that such com...
作者:Sean Clark
来源:[J].Algebraic & Geometric Topology, 2017, Vol.17 (5), pp.2961-3005
摘要:We show that the quantum covering group associated to o s p ( 1 | 2 n ) has an associated colored quantum knot invariant à la Reshetikhin–Turaev, which specializes to a quantum knot invariant for o s p ( 1 | 2 n ) , and to the usual quantum knot invariant for s o ( 1 + 2 n )...
作者:Shengkui Ye
来源:[J].Algebraic & Geometric Topology, 2018, Vol.18 (2), pp.1195-1204
摘要:Let M r be a connected orientable manifold with the Euler characteristic χ ( M ) ≢ 0 mod 6 . Denote by SAut ( F n ) the unique subgroup of index two in the automorphism group of a free group. Then any group action of SAut ( F n ) (and thus the special linear group SL n ...
作者:Lorenzo Guerra
来源:[J].Algebraic & Geometric Topology, 2017, Vol.17 (2), pp.957-982
摘要:We describe a Hopf ring structure on ⊕ n ≥ 0 H ∗ ( Σ n ; ℤ p ) , discovered by Strickland and Turner, where Σ n is the symmetric group of n objects and p is an odd prime. We also describe an additive basis on which the cup product is explicitly determined, compute ...

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