PoorMansNamedSemaphore.cs

internal static class Program
{
    private static readonly SemaphoreSlim InstanceCheck = new SemaphoreSlim(0, 1);
    private static readonly SemaphoreSlim ShutdownCheck = new SemaphoreSlim(0, 1);

    internal static async Task Main(string[] args)
    {
        var thread = new Thread(() =>
                                {
                                    using (var instanceLock = new Mutex(false, @"Global\mutex name"))
                                        if (instanceLock.WaitOne(1000))
                                            try
                                            {
                                                InstanceCheck.Release();
                                                ShutdownCheck.Wait();
                                            }
                                            finally
                                            {
                                                instanceLock.ReleaseMutex();
                                            }
                                });
        try
        {
            thread.Start();
            if (!InstanceCheck.Wait(1000))
            {
                Console.WriteLine("Another instance is already running.");
                return;
            }
            // ...
        }
        finally
        {
            ShutdownCheck.Release();
            thread.Join(100);
        }
    }
}