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The heat kernel expansion can be used as a tool to obtain the effectivegeometric quantities in fuzzy spaces. Generalizing the efficient methodpresented in the previous work on the global quantities, it is applied to theeffective local geometric quantities in compact fuzzy spaces. Some simple fuzzyspaces corresponding to singular spaces in continuum theory are studied asspecific examples. A fuzzy space with a non-associative algebra is alsostudied.Comment: Two references added, typos, 26 pages, many figures, LaTe

Effective local geometric quantities in fuzzy spaces from heat kernel expansions