Indefinite Stein fillings and PIN(2)-monopole Floer homology

Francesco Lin ^[1]
1. [1] Columbia University
  
  Columbia University
  
  Estados Unidos
Localización: Selecta Mathematica, New Series, ISSN 1022-1824, Vol. 26, Nº. 2, 2020
Idioma: inglés
DOI: 10.1007/s00029-020-0547-y
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Resumen
- We introduce techniques to study the topology of Stein fillings of a given contact three-manifold (Y,ξ) which are not negative definite. For example, given a spinc rational homology sphere (Y,s) with s self-conjugate such that the reduced monopole Floer homology group HM∙(Y,s) has dimension one, we show that any Stein filling which is not negative definite has b+2=1 or 2, and b−2 is determined in terms of the Frøyshov invariant. The proof of this uses Pin(2)-monopole Floer homology. More generally, we prove that analogous statements hold under certain assumptions on the contact invariant of ξ and its interaction with Pin(2)-symmetry. We also discuss consequences for finiteness questions about Stein fillings.