Spin Borromean surgeries

Realizing isomorphisms between first homology groups of closed 3-manifolds by borromean surgeries

We refine Matveev's result asserting that any two closed oriented 3-manifolds can be related by a sequence of borromean surgeries if and only if they have isomorphic first homology groups and linking pairings. Indeed, a borromean surgery induces a canonical isomorphism between the first homology groups of the involved 3-manifolds, which preserves the linking pairing. We prove that any such isomorphism is induced by a sequence of borromean surgeries. As an intermediate result, we prove that a given algebraic square finite presentation of the first homology group of a 3-manifold, which encodes t…

Borromean surgery formula for the Casson invariant

It is known that every oriented integral homology 3-sphere can be obtained from S^3 by a finite sequence of Borromean surgeries. We give an explicit formula for the variation of the Casson invariant under such a surgery move. The formula involves simple classical invariants, namely the framing, linking number and Milnor's triple linking number. A more general statement, for n independent Borromean surgeries, is also provided, which involves an additional cubic expression in some linking numbers of the surgery link.

Borromean surgery equivalence of spin 3-manifolds with boundary

Matveev introduced Borromean surgery on 3-manifolds, and proved that the equivalence relation on closed, oriented 3-manifolds generated by Borromean surgeries is characterized by the first homology group and the torsion linking pairing. Massuyeau generalized this result to closed, spin 3-manifolds, and the second author to compact, oriented 3-manifolds with boundary. In this paper we give a partial generalization of these results to compact, spin 3-manifolds with boundary.

Heegaard Floer手术公式与美容手术

Heegaard Floer Surgery Formula and Cosmetic Surgeries

本文利用Heegaard Floer同调公式，证明了特定结的美容手术系数必须大于1，并且非整数手术不会与原流形同胚。

Geography of spin symplectic 4-manifolds with abelian fundamental group

In this paper, results of J. Park and of B.D Park and Szabo on simply connected symplectic 4-manifolds are re-proven and extended to non-simply connected manifolds using Luttinger surgeries.

Spin-cobordisms、surgeries与费米子模bootstrap

Spin-cobordisms, surgeries and fermionic modular bootstrap

本文研究了具有全局有限群对称性的一般费米子量子场论，提出通过入流从体3d iTQFT直接确定模变换的方法，并基于spin-cobordisms分类提供了spin-bordism不变量的显式组合表达式，探讨了't Hooft反常对红外共形场论谱的约束。