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Rot fungi found in the exterior panelling of buildings must be able to withstand very varying conditions of temperature and moisture. In this study we have exposed wood samples with the brown-rot fungus Gloeophyllum scpiarium, often found in exterior panelling, to high and low temperatures, oxygen depletion, and drying. The activity of the fungi before and after the exposures was monitored by isothermal m icrocalori metry at 25 °C in order to assess the rate and level of recovery. The activity of the fungus was not greatly influenced by exposures (o 6, 37 and 45 °C. Higher temperatures (55 and 60°C) resulted in an initial period of low activity followed after 20-1 OOh by a recovery back to approximately the prc-exposure level. After Ih exposure to 65 °C no activity could be detected so the lethal temperature for this fungus is in the range of 60-65 °C. Low temperatures (-23 °C) resulted in reduced activity during 10-20h. The activity of the fungus decreased in closed vessels as a result of an increased concentration of carbon dioxide. When fresh air was admitted the activity wenl back to the level before the exposure. Wetting after drying returned the activity to the level it had before the drying.

In this paper, we introduce the annular instanton Floer homology which is defined for links in a thickened annulus. It is an analogue of the annular Khovanov homology. A spectral sequence whose second page is the annular Khovanov homology and which converges to the annular instanton Floer homology is constructed. As an application of this spectral sequence, we prove that the annular Khovanov homology detects the unlink in the thickened annulus (assuming all the components are null-homologous). Another application is a new proof of Grigsby and Ni's result that tangle Khovanov homology distinguishes braids from other tangles.

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We prove that any link in S 3 whose Khovanov homology is the same as that of a Hopf link must be isotopic to that Hopf link. This holds for both reduced and unreduced Khovanov homology, and with coefficients in either Z or Z/2Z. Khovanov homology [Kho00] associates to each link L ⊂ S 3 a bigraded group Kh * , * (L), whose graded Euler characteristic recovers the Jones polynomial V L (q), as well as a reduced variant Kh * , * red (L) [Kho03]. It is known to detect the unknot [KM11], the n-component unlink for all n [BS15], and the trefoils [BS18]. In this note we prove the same for the Hopf links H ± , which are oriented so that the two components have linking number ±1. Thenwhere Z (h,q) is a copy of Z in bigrading (h, q). The reduced Khovanov homology of a link depends on a choice of distinguished component, which we generally suppress from the notation, but we have Kh red (H + ; Z) ∼ = Z (0,1) ⊕ Z (2,5) and Kh red (H − ; Z) ∼ = Z (0,−1) ⊕ Z (−2,−5) regardless of this choice.Theorem 1. Let L be a link in S 3 such that either Kh(L) ∼ = Kh(H ± ) or Kh red (L) ∼ = Kh red (H ± ) as bigraded groups, with coefficients in either Z or Z/2Z. Then L = H ± .

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