Local rigidity problem of smooth group actions

2017 ◽  
Vol 30 (2) ◽  
pp. 207-233
Author(s):  
Masayuki Asaoka
Keyword(s):  
Group Actions ◽  
Local Rigidity ◽  
Smooth Group Actions

scholarly journals SMOOTH GROUP ACTIONS ON 4-MANIFOLDS AND SEIBERG–WITTEN INVARIANTS

1998 ◽  
Vol 09 (08) ◽  
pp. 957-973 ◽  
Author(s):  
FUQUAN FANG
Keyword(s):  
Finite Group ◽  
Dirac Operator ◽  
Lie Group ◽  
Group Actions ◽  
Witten Invariant ◽  
Compact Lie Group ◽  
Smooth Group Actions ◽  
Structure Formula ◽  
A Finite Group

In this paper we study the Seiberg–Witten invariants of 4-manifold acted on by a finite group (or a compact Lie group). Among other things, we have: Let X be a smooth closed 4-dimensional ℤp-manifold, where p is a prime. Suppose H1(X,ℝ) = 0 and [Formula: see text] where [Formula: see text]. If ℤp acts trivially on the space [Formula: see text] of self dual harmonic 2-forms, then, for any ℤp-equivariant Spin c-structure [Formula: see text] on X, the Seiberg–Witten invariant satisfies [Formula: see text] provided [Formula: see text] for j = 0,1,…,p-1, where [Formula: see text], DA: Γ(W+) → Γ (W-) is the equivariant Dirac operator determined by [Formula: see text] for an equivariant connection A on det W+.

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