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Creators/Authors contains: "Wiringa, RB"

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  1. ; ; (, Mathematical Proceedings of the Cambridge Philosophical Society)
    Abstract We discuss the Singer conjecture and Gromov–Lück inequality$$\chi\geq |\sigma|$$for aspherical complex surfaces. We give a proof of the Singer conjecture for aspherical complex surfaces with residually finite fundamental group that does not rely on Gromov’s Kähler groups theory. Without the residually finiteness assumption, we observe that this conjecture can be proven for all aspherical complex surfaces except possibly those in Class$$\mathrm{VII}_0^+$$(a positive answer to the global spherical shell conjecture would rule out the existence of aspherical surfaces in this class). We also sharpen the Gromov-Lück inequality for aspherical complex surfaces that are not in Class$$\mathrm{VII}_0^+$$. This is achieved by connecting the circle of ideas of the Singer conjecture with the study of Reid’s conjecture. 
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    Free, publicly-accessible full text available July 17, 2026
  2. ; (, The Journal of Geometric Analysis)
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  3. ; (, Communications in Analysis and Geometry)
    Abstract. For compact complex surfaces (M^4,J) of Kaehler type, it was previously shown (LeBrun 1999) that the sign of the Yamabe invariant Y (M) only depends on the Kodaira dimension Kod(M,J). In this paper, we prove that this pattern in fact extends to all compact complex surfaces except those of class VII. In the process, we also reprove a result from (Albanese 2021) that explains why the exclusion of class VII is essential here. 
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