Fact verification is a challenging task that requires simultaneously reasoning and aggregating over multiple retrieved pieces of evidence to evaluate the truthfulness of a claim. Existing approaches typically (i) explore the semantic interaction between the claim and evidence at different granularity levels but fail to capture their topical consistency during the reasoning process, which we believe is crucial for verification; (ii) aggregate multiple pieces of evidence equally without considering their implicit stances to the claim, thereby introducing spurious information. To alleviate the above issues, we propose a novel topic-aware evidence reasoning and stance-aware aggregation model for more accurate fact verification, with the following four key properties: 1) checking topical consistency between the claim and evidence; 2) maintaining topical coherence among multiple pieces of evidence; 3) ensuring semantic similarity between the global topic information and the semantic representation of evidence; 4) aggregating evidence based on their implicit stances to the claim. Extensive experiments conducted on the two benchmark datasets demonstrate the superiority of the proposed model over several state-of-the-art approaches for fact verification. The source code can be obtained from https://github.com/jasenchn/TARSA.